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, 2-Lek_Yқtimaldyқtar teoriyasy.doc.
F.Harari
THEORY OF GRAPHS
M .: Mir, 1973, 300 pages.
Recently, graph theory has attracted more and more attention from specialists in various fields of knowledge. Along with its traditional applications in such spiders as physics, electrical engineering, chemistry, it also penetrated into the sciences that were previously considered far from it - economics, sociology, linguistics, and others. probabilities. A particularly important relationship exists between graph theory and theoretical cybernetics (especially automata theory, operations research, coding theory, game theory).
The theory of graphs is widely used in solving various problems on computers.
In recent years, the topics of graph theory have become much more diverse; the number of publications increased dramatically.
This book was written by one of the prominent specialists in discrete mathematics. Despite the small volume and concise nature of the presentation, the book quite fully covers the current state of graph theory. It will undoubtedly be useful for students of universities and technical universities and will undoubtedly be of interest to a wide range of researchers involved in applications of discrete mathematics.
Translation Editor's Preface 6
Introduction 9
Chapter 1. Opening! thirteen
Königsberg bridges problem 13
Electrical circuits 14
Chemical isomers 15
"Around the World" 16
Four Colors Hypothesis 17
Graph theory in the twentieth century 18
Chapter 2. Columns 21
Graph types 21
Routes and Connectivity 26
Degree 27
Ramsey problem 28
Extreme graphs 30
Intersection graphs 33
Graph operations 35
Exercises 38
Chapter 3. Blocks 41
Articulation points, bridges and blocks 41
Block graphs and articulation point graphs 45
Exercises 46
Chapter 4. Trees 48
Description of trees 48
Centers and centroids 51
Block and articulation trees 53
Independent cycles and cocycles 54
Matroids 57
Exercises 59
Chapter 5. Connectivity 60
Connectivity and edge connectivity 60
Graphic variants of Menger's theorem 64
Other variants of Menger's theorem 70
Exercises 74
Chapter 6. Partitions 76
Exercises 81
Chapter 7. Traversing Graphs 83
Euler Graphs 83
Hamiltonian graphs 85
Exercises 88
Chapter 8. Edge graphs 91
Some properties of edge graphs 91
Characterization of edge graphs 94
Special edge graphs 99
Edge graphs and traversals 101
Total Counts 103
Exercises 104
Chapter 9. Factorization 106 1-factorization 106 2-factorization 111
Woodiness
113
Exercises 116
Chapter 10. Coatings 117
Covers and independence 117
Critical vertices and edges 120
Costal nucleus 122
Exercises 124
Chapter 11. Planarity
126
Plane and Planar Graphs 126
Outerplanar graphs 131
The Pontryagin-Kuratovsky theorem 133
Other characterizations of plenary graphs 138
Genus, thickness, size, number of crosses 141
Exercises 148
Chapter 12. Coloring Pages 151
Chromatic number 152
Five-color theorem 155
The four-color hypothesis 156
Hewood Card Coloring Theorem 162
Uniquely Colorable Graphs 164
Critical columns 167
Homomorphisms 169
Chromatic polynomial 172
Exercises 175
Chapter 13. Matrices 178
Adjacency Matrix 178
Incident Matrix 180
Loop Matrix 183
Overview of additional properties of matroids 186
Exercises 187
Chapter 14. Groups 189
The group of automorphisms of a graph 193
Operations on Substitution Groups 194
Graph composition group 195
Counts with this group 198
Symmetric graphs 201
Stronger Symmetry Graphs 204
Exercises 206
Chapter 15. Enumerations 209
Marked boxes 209
Polya's enumeration theorem 211
Enumeration of columns 216
Tree listing 219
Enumeration theorem for a power group 224
Solved and Unsolved Graph Enumeration Problems 225
Exercises 230
Chapter 16. Digraphs 232
Digraphs and Connectivity 232
Oriented duality and contourless digraphs 234
Digraphs and Matrices 237
Overview on Tournament Recovery 244
Exercises 244
Appendix I. Graph diagrams 248
Appendix II. Digraph Charts 260
Appendix III. Tree diagrams 266
References and index 268
Symbol Index 291
Index 293
Subject index graph automorphism 190 basis of cocycles 55
Cycles 55 block 41 valency of vertices 27 vertex of graph 22, 126
- isolated 28
- incident to rib 22
- end 28
- critical 121
- fixed 201
- digraph 232
- peripheral 51
- central 51
- centroid 52 vertex base 237 vertices like 201
- adjacent 22, 213 weight of vertex 52 weight of function 213 branch 56
- to apex 52 vortex 187 exterior of cycle 134 convex polyhedron 130 Ulam hypothesis 25, 26, 48, 58, 202,
244
- Hadwiger 161, 162
- four colors 151, 156-162, 164,
167, 172 graph homomorphism 169
- full order l 169
- elementary 169 homomorphic image of a graph 196 boundary operator 54 face 127
- external 127
- internal 127 count asymmetric 190
- acyclic 48
- basic 132
- endless 36
- blocks 45
- - and articulation points 53
- vertex critical 121
- vertex symmetric 201
- external planar 131
- - maximum 131
- quite incoherent 28
- Hamilton 85
- geometrically dual 138
- David 29
- dicotyledonous 31
- additional 29
- intervals 35
- click 34
- combinatorially dual 139
- critical 167
- cubic 28
- Levy 205, 206
- McGe 205
- directional 23
- inseparable 41
- irreducible 123
- uniquely paintable 164
- single-cycle 58
- intersections 33
- Petersen 113
- planar 127
- - maximum 128
- flat 127
- subdivisions 101
- full 29 count full bipartite 32
- - n-part 37
- semi-removable 123
- tagged 23
- arbitrarily Hamiltonian 89
- - passable 89
- simple 197
- rib-critical 121
- rib-regular 202
- rib-symmetric 201
- costal 91, 94
- - iterated 91
- regular 28
- self-complementary 29
- convertible 123
- symmetrical 201
- compound 197
Toroidal 142
- total 103
- points of articulation 45
- trivial 22
- Khivuda 204
- Euler 83
- n-paintable 152
- n-transitive 204
- n-unitransitive 204
- n-chromatic 152
- \\ alpha-permutation 206 graph composition 196 graphoid 58 homeomorphic graphs 132
- isomorphic 24, 190
- cospectral 188 group 189
- column 190
- vertex 190
- dihedral 195
- alternating 195
- configurations 213
- steam room 217
- - reduced 218
- substitutions 190
- costal 191
- symmetric 195
- power 194
- identical 195
- cyclic 195 groups identical 190
- isomorphic 190 wood 48
- blocks and points of articulation 54
- root 219
- with a hanging root 220
- incoming 235
- outgoing 235 diagonal of block 47
"Hasse diagram" 73 diameter 27 route length 27 vertex addition 25
- edges 25 complement of graph 29 reachability 133 woodiness of graph 113 arc 23, 232 animal 227 lattice paving, 2, 227 star (paw, bunch) 32 isomorphism 24 invariant 24 incidence of an edge and a vertex 22 graph distortion 149 source 235 map flat 127
- - with root edge 227 square of graph 27 square root of graph 38 cell 204 number of points 243 graph clicks 34 coboundary 55 border operator 54 code tree 56 wheel 63 complex 20 graph composition 37, 196
- groups 194 components 27
- odd 108
- one-sided 233
- strong 233
- weak 233 condensation 234 circuit 233
- Euler 240 configuration 213 conjunction 40, 243 crown of graphs 198 cocycle 55 coarseness (graininess, roughness) 146 Burnside lemma 212, 214 forest 48 matrix line 71 linear subgraph of graph 180
Orgraph 179
Route 26
- closed 26
- imperfect 119
- open 26
- perfect 119
- Y-reducible 120 reachability matrix 238
- ISO incidents
- cocycles 184
- bypasses 238
- half-degrees of approach 239
- - outcome 239
- sparse 241
- adjacencies of column 179
- - digraph 237
- cycles 183 matrix tree theorem 178,
181, 239 matroid 57
- binary 188
- graphic 180
- graphic 180
- cocycles of count 57
- graph cycles 57
- Euler 188 tree polynomial graph 187 vertex set 22
- externally stable 118
- internally stable 118
- independent 57, 108, 118
- separating 64
- edges 22 bridge 41 multigraph 23 hereditary property 119 epigraph 24 independent units of the matrix 71 girth 27 union of graphs 36 one-color class 152 necklace 212-215, 224, 225 vertex neighborhood 197
- closed 197 environment 27 orbit 211 digraph 232
- contourless 235
- counterfunctional 236 incoherent digraph 233
- reverse 234
- one-sided 233
- primitive 246
- costal 245
- strong 233
- weak 233
- strictly one-sided 244
- - weak 244
- functional 236
- Euler 240 orientation of the graph 246 skeleton 55 pair of connections 62 matching 119
- the largest 119 listing range for 213 configurations
- - - figures 213 loop 23 subgraph 24
- linear 180
- spanning 24
- spawned 24
- even 227 vertex coverage 117
- edge 117 polyhedron 127 full coloring 170 full set of invariants 24 graph semigroup 208 half-contour 233 half-route 233 half-path 233 half-degree of entry 232
- outcome 232 group order 190 n-path follower 204
principle of oriented duality 234, 235 product of graphs 36
- groups 190
- element-wise 239 cocycle 55 space
- cycles 55 pseudograph 23 path 233 graph partition 76
- graphic 76
- numbers 76 cut 55 rank cocyclic 56
- cyclic 55 simplex dimension 20 distance in column 27
- - digraph 233 coloring of graph 152
- flat card 156
- full 170
- ribs 159
- t colors 172 edges multiples of 23
- independent 108
- similar 01, 2
- adjacent 22 edges of graph 22
- incident to vertex 22
- critical 121
- broken 101
- symmetrical 221 kinds of graph 142
- polyhedron 142 network 70 system of various representatives
72 stabilizer 211 vertex degree 27
- column 27
- groups 190
- ribs 202 drain 235 contraction 137
- elementary 137 sum of columns 37
- groups 193 Wienet-Cauchy theorem 181
- on the interpolation of homomorphisms
171
- about five colors 151, 155, 156
- Poya transfers 211-215, 217,
218
- - power group 224
- Hewood on the coloring of Maps 162-164
- BEST 240 graph thickness 145 articulation points 41 transitive triplets 241 triangles 26
- odd 95
- even 95 tournament 241 competition tournament 245 theta graph 85 removal of vertex 25
- edges 25 stacking graph 126 equation of dissimilarity characteristics for trees 221
- Euler-Poincaré 57 factor of graph 106 factorization of graph 106 figure 213 Otter's formula 222
- Euler for polyhedra 127 connectivity function 62 connectivity 60
- local 66
- one-sided 233
- rib 60
- strong 233
- weak 233 chord 55 chromatic class 159
- polynomial 173 color graph of group 199 center of graph 51
tree centroid 52 disjoint chains 64
- edge-non-intersecting 64 chain 26
- alternating 109
- geodetic 27
- simple 26 cycle 26
- Hamilton 85
- column yes 58
- matroid 57
- simple 26
- Euler 83 cyclic triple 241 cyclic vector of a graph 54 cyclic group index 212 achromatic number 170
- independence vertex 118
- - costal 118
- intersections 33
- cover of the vertex 117
- - costal 117
- Ramsey 30
- - rib 104
- crosses 148
- Hadwiger 177
- chromatic 152
- n-chromatic 177 exponentiation 208 eccentricity 51 elements of the graph 103 elements adjacent 103 endomorphism of the graph 208 vertex core 125
- edge 122 chain, 54 base, 1, 237 skeleton, 1, 127 chain, 1, 54 lattice, 2, 227 lattice, 3, 227 n-cell 204 n-component 63 n-cube 37 n-path 204 n-coloring 152
- edge 159 n-connectivity 63 n-factor 106 n-factorization 106
P-set 119
Translated from English. and foreword. V.P. Kozyrev. Ed. G.P. Gavrilova. Ed. 2nd. - M .: Editorial URSS, 2003 .-- 296 p. - ISBN 5-354-00301-6. Recently, graph theory has attracted more and more attention from specialists in various fields of knowledge. Along with its traditional applications in such sciences as physics, electrical engineering, chemistry, it also penetrated into the sciences that were previously considered far from it - economics, sociology, linguistics, etc. Close contacts of graph theory with topology, group theory and theory have long been known probabilities. A particularly important relationship exists between graph theory and theoretical cybernetics (especially automata theory, operations research, coding theory, game theory). The theory of graphs is widely used in solving various problems on computers. In recent years, the topics of graph theory have become much more diverse; the number of publications increased dramatically. This book was written by one of the prominent specialists in discrete mathematics. Despite the small volume and concise nature of the presentation, the book quite fully covers the current state of graph theory. It will undoubtedly be useful for university and technical university students and will undoubtedly be of interest to a wide range of researchers involved in the applications of discrete mathematics.
Introduction Opening!
Königsberg bridges problem
Electrical circuits
Chemical isomers
"Around the world"
The four-color hypothesis
Graph theory in the twentieth century Graphs
Graph types
Routes and connectivity
Degrees
Ramsey problem
Extreme graphs
Intersection graphs
Graph operations
Exercises Blocks
Articulation points, bridges and blocks
Block graphs and articulation point graphs
Exercises Trees
Description of trees
Centers and centroids
Block and articulation trees
Independent cycles and cocycles
Matroids
Exercises Connectivity
Connectivity and edge connectivity
Graphic variants of Menger's theorem
Other variants of Menger's theorem
Exercises Partitions
Exercises Graph traversal
Euler graphs
Hamiltonian graphs
Exercises Edge graphs
Some properties of edge graphs
Characterization of edge graphs
Special edge graphs
Edge graphs and traversals
Total graphs
Exercises Factorization
1-factorization
2-factorization
Woodiness
Exercises Coating
Covers and independence
Critical vertices and edges
Costal nucleus
Exercises Planarity
Plane and planar graphs
Outerplanar graphs
The Pontryagin - Kuratovsky theorem
Other characterizations of planar graphs
Genus, thickness, size, number of crosses
Exercises Coloring Pages
Chromatic number
The five-color theorem
The four-color hypothesis
Hewood's card coloring theorem
Uniquely Colorable Graphs
Critical graphs
Homomorphisms
Chromatic polynomial
Exercises Matrices
Adjacency matrix
Incident matrix
Loop matrix
An overview of the additional properties of matroids
Exercises Groups
Graph automorphism group
Operations on substitution groups
Composition graph group
Graphs with a given group
Symmetric graphs
Stronger Symmetry Graphs
Exercises Enumerations
Labeled graphs
Polya's enumeration theorem
Enumerating graphs
Tree enumeration
Power group enumeration theorem
Solved and unsolved problems of enumerating graphs
Exercises Digraphs
Digraphs and connectivity
Oriented duality and contourless digraphs
Digraphs and Matrices
Tournament Recovery Review
Exercises application
Graph charts
Digraph charts
Tree diagrams References and index
Index of symbols
Subject index
2012-07-26 at 10:21
 |
Alekseev V.V., Gavrilov G.P., Sapozhenko A.A. (ed.) Graph theory. Coverings, styling, tournaments. Collection of translations - M.: Mir, 1974.- 224 p. |
Content
Foreword
List of symbols
CHAPTER 1. Ways to represent graphs
1.1. General representation of arbitrary graphs
1.2. Defining graphs using matrices
1.3. Binary graph representation
1.4. Binary relations for graphs
1.5. Defining a graph in the form of a formal quadratic form
1.6. Analytic representation of graphs
CHAPTER 2. Problems of Optimal Representation of Graphs
2.1. Representing graphs using data structures
2.2. Tree view
2.3. Estimation of the number of operations of algorithms
2.4. Optimal encoding of arithmetic graphs
CHAPTER 3. Elements of the theory of complexity of algorithms for problems on graphs
3.1. Basic concepts
3.2. Classes P and NP
3.3. Polynomial Reducibility and JVP-Complete Problems
3.4. Proof of Results on VP-Completeness
3.5. Applying WP-completeness theory to problem analysis
CHAPTER 4. Operation on ordinary graphs
4.1. Operations on vertices to edges
CHAPTER 5. Reconstruction of graphs
5.1. Isomorphism
5.2, Invariants
5.3. Isomorphism problems
5.4. Recovery problems. Existence and uniqueness
5.5. Ulam hypothesis
5.6. Algorithm for restoring graphs from an admissible set
5.7. Existence and uniqueness theorem
5.8. Minimal sets of subgraphs
Conclusion
Bibliography
2012-07-26 at 10:35
 |
Donets G.A., Shor N. 3. Algebraic approach to the problem of coloring plane graphs - Kyiv: Naukova Dumka, 1982. - 144 p. |
Content
The main stages of the proof of the four-color hypothesis.
Historical reference.
Evidence from Tate, Kempe, and Hewood.
Reducibility of graphs and configurations.
Four types of reducibility of the configuration.
The neutralization method and its development.
Hewood equations.
The problem of four colors and a group of substitutions.
Systems of equations modulo.
Algebraic inequalities related to the coloring of triangular graphs with three colors.
Algorithms for coloring plane graphs with four colors.
Combinatorics of matchings and coloring of graphs.
Pfaffian and perfect graph matchings.
Counting the number of matchings of a graph dual to a maximal planar graph.
Counting the coefficients of some polynomials modulo 2 and modulo 3 using formulas associated with counting the number of matchings.
Analysis of the system of equations modulo.
The problem of choosing and coloring graphs.
On one algorithm for coloring plane graphs.
Derivation of the system of equations. A special case.
Some conditions for the solvability of the canonical system.
General condition for the solvability of the system.
Study of the system of equations for the general case.
Conditions for solving the general canonical system and questions of constructing a coloring algorithm.
2012-07-26 at 10:44
Content
From author 4
Introduction 5
CHAPTER 1. IDENTIFICATION 12
§1.1. Ordinary columns 12
§ 1.2. Isomorphism 15
§ 1.3. Invariants 21
§ 1.4. Calculation of invariants 31
§ 1.5. Isomorphism problem 41
§ 1.6. Some Applications of Density and Leakage 47
§ 1.7. Algorithms for Density, Leakage, and Isomorphism 56
§ 1.8. Density and Leakage Estimates. Count Turan 65
§ 1.9. Optimal and critical graphs 73
§ 1.10. Recovery problems 80
CHAPTER 2. CONNECTIVITY 96
§ 2.1. Routes 96
§2.2. Blocks 108
§2.3. Trees 118
§ 2.4. Matching and bipartite graphs 125
§ 2.5.1-connected graphs 137
§ 2.6. Weighted Graphs and Metric 149
§ 2.7. Multigraphs 162
§ 2.8. Euler chains and cycles 171
§ 2.9. Ribs coloring pages 176
CHAPTER 3. CYCLOMATICS 188
§ 3.1. Frames and cuts 188
§ 3.2. Sugraf Space 197
§ 3.3. Incident, Cut and Cycle Matrices 202
§ 3.4. Graphs with Given Cuts and Cycles 211
§ 3.5. Topological graphs 225
§ 3.6. Planarity 234
§ 3.7. Intersection Control 252
§ 3.8. Hadwiger Hypothesis 262
§ 3.9. Plane triangulation coloring pages 275
§ 3.10. Perfect Counts 291
CHAPTER 4. ORIENTATION 305
§ 4.1. Finite General Graphs 305
§ 4.2. Reachability 314
§4.3. Kernels 332
§ 4.4. Orientability 342
§ 4.5. Transit 350
Adding. Boolean Methods in Graph Theory 363
Conclusion 379
2012-07-26 at 10:55
 |
Kalmykov G.I. Tree classification of labeled graphs. - M .: FIZMATLIT, 2003 .-- 192 p. - ISBN 5-9221-0333-4. |
Content
Foreword for theoretical physicists
Preface by the author
Chapter I Classification of Labeled Graphs
§1. Semi-ordering of marked root trees. Pseudo-skeleton and skeleton of a connected labeled graph
§ 2. The maximum epigraph of a tree. Tree classification of connected labeled graphs
§ 3. Tree classification of tagged trees and other classifications of tagged trees
§ 4. Maximal isomorphism of labeled rooted trees
§ 5. Classes of maximally isomorphic rooted labeled trees
§ 6. Classification of all (n + 1) -vertex labeled graphs
§ 7. Counting the number of connected labeled graphs with an even and odd number of edges
Chapter II Representation in tree form of the coefficients of power expansions of thermodynamic quantities
§ 1. Tree representation of the Ursell function
§ 2. Wood sums for the expansion coefficients of pressure and density by degrees of activity
§ 3. Representation in tree form of the coefficients of expansions in degrees of activity for truncated distribution functions
Chapter III Some problems of the transition to the thermodynamic limit
Chapter IV Expansions in terms of degrees of activity in the thermodynamic limit
§ 1. Decompositions of pressure and density
§ 2. Expansions of distribution functions
§ 3. Estimation of the radius of convergence of expansions of pressure and density in degrees of activity in the case of a nonnegative potential
Chapter V Analytical Continuations of Virial Decomposition and Decomposition in Degrees of Activity
Chapter VI About the expansions of density and specific volume by degrees of activity
Chapter VII Representation of virial coefficients in the form of polynomials in tree sums
§ 1. The case of tree sums representing the coefficients `b_n (beta)`
§ 2. The case of tree sums representing the coefficients ʻa_n (beta) `
Chapter VIII The problem of asymptotic catastrophe and its solution using the method of tree sums
§ 1. Decompositions in activity
§ 2. Virial coefficients
Application. Computing the integrals from Example IV.2
Bibliography
Designations
Subject index
2012-07-26 at 11:48
 |
Cameron P., van Lint J. Graph theory, coding theory and block diagrams - M.: Nauka, 1980, 140 pp. |
Content
Translator's Preface 4
Introduction 5
1. Brief introduction to circuit theory 6
2. Strongly Regular Graphs 17
3. Quasi-symmetrical circuits 24
4. Strongly Regular Triangle-Free Graphs 29
5. Circuit polarities 37
6. Expansion of graphs 41
7. Codes 47
8. Cyclic sneakers 54
9. Threshold decoding 59
10. Reed - Muller codes 62
11. Self-orthogonal codes and schemes 67
12. Quadratic Residue Codes 73
13. Symmetric codes over GFC) 83
14. Nearly perfect binary codes and evenly packed codes 88
15. Associative schemes 97
Literature 109
Additions from the second edition 114
Further reading 134
Index 137
2012-07-26 at 11:59
 |
Christofides N. Graph Theory. Algorithmic approach. Per. from English - M.: Mir, 1978, 432 p. |
Content
Foreword
Chapter 1. Introduction
1. Graphs. Definition
2. Paths and routes
3. Loops, oriented loops and loops
4. Degrees of apex
5. Subgraphs
6. Types of graphs
7. Strongly connected graphs and graph components
8. Matrix representations
9. Tasks
10. References
Chapter 2. Reachability and Connectivity
1. Introduction
2. Matrix of reachability and contrareachability
3. Finding strong components
4. Bases
5. Problems associated with limited reachability
6. Tasks
7. References
Chapter 3. Independent and dominant sets.
Covering set problem
1. Introduction
2. Independent sets
3. Dominant sets
4. The problem of the smallest coverage
5. Applications of the coverage problem
6. Tasks
7. References
Chapter 4. Coloring
1. Introduction
2. Some theorems and estimates related to chromatic numbers
3. Exact coloring algorithms
4. Approximate coloring algorithms
5. Generalizations and applications
6. Tasks
7. References
Chapter 5. Placement of centers
1. Introduction
2. Separations
3. Center and radius
4. Absolute center
5. Algorithms for finding absolute centers
6. Multiple centers (p-centers)
7. Absolute p-centers
8. Algorithm for finding absolute p-centers
9. Tasks
10. References
Chapter 6. Placing medians in a graph
1. Introduction
2. Median of the graph
3. Multiple medians (p-medians) of a graph
4. Generalized p-median of a graph
5. Methods for solving the p-median problem
6. Tasks
7. References
Chapter 7. Trees
1. Introduction
2. Construction of all spanning trees of the graph
3. Shortest skeleton (SST) graph
4. Steiner's problem
5. Tasks
6. References
Chapter 8. Shortest Paths
1. Introduction
2. The shortest path between two given vertices s and t
3. Shortest paths between all pairs of vertices
4. Detection of cycles of negative weight
5. Finding the K shortest paths between two given vertices
6. The shortest path between two given vertices in a directed acyclic graph
7. Problems close to the shortest path problem
8. Tasks
9. References
Chapter 9. Cycles, cuts and Euler's problem
1. Introduction
2. Cyclomatic number and fundamental cycles
3 .. Cuts
4. Matrices of cycles and cuts
5. Euler cycles and the problem of the Chinese postman
6. Tasks
7. References
Chapter 10. Hamiltonian cycles, chains and the traveling salesman problem
1. Introduction
PART I
2. Hamiltonian cycles in a graph
3. Comparison of search methods for Hamiltonian cycles
4. Simple planning task
PART II
5. The traveling salesman problem
6. The traveling salesman problem and the shortest skeleton problem
7. The traveling salesman problem and the assignment problem
8. Tasks
9. References
10. Appendix
Chapter 11. Streams in networks
1. Introduction
2. The main problem of the maximum flow (from s to t)
3. Simple versions of the maximum flow problem (from s to t)
4. Maximum flow between each pair of vertices
5. Minimum cost flow from s to t
6. Streams in payoff graphs
7. Tasks
8. References
Chapter 12. Matching, Transport Problem, and Assignment Problem
1. Introduction
2. Largest matchings
3. Maximum matchings
4. The assignment problem
5. The general problem of constructing a spanning subgraph with prescribed degrees
6. The problem of covering
7. Tasks
8. References
Appendix 1. Search Methods Using Decision Trees
1. Search principle using a decision tree
2. Some examples of branching
3. Types of search using decision tree
4. Application of boundaries
5. Branching functions
Subject index
2012-07-26 at 12:25
 |
Mainika E. Optimization algorithms on networks and graphs. Per. from English. - M.: Mir, 1981, 328 p. |
Content
Translation Editor's Foreword
Foreword
Glana 1. Introduction to the theory of graphs and networks
1.1. Introductory remarks
1.2. Some concepts and definitions
1.3. Linear programming
Exercises
Literature
Chapter 2. Algorithms for constructing trees
2.1. Spanning Tree Algorithms
2.2. Algorithm for constructing a maximum oriented forest
Exercises
Literature
Chapter 3. Path finding algorithms
3.1. Shortest Path Search Algorithm
3.2. All Shortest Path Search Algorithms
3.3. Shortest Path Search Algorithm
3.4. Finding other optimal paths
Exercises
Literature
Chapter 4. Streaming Algorithms
4.1. Introduction
4.2. Maximum flow search algorithm
4.3. Algorithm for finding the minimum cost flow
4.4. Defect Algorithm
4.5. Dynamic flow search algorithm
4.6. Amplified streams
Exercises
Literature
Chapter 5. Algorithms for finding pairing and coverage
5.1. Introduction
5.2. Algorithm for solving the problem of maximum power steam control
5.3 Algorithm for choosing a matching with maximum weight
5.4. Minimum Weight Coverage Construction Algorithm
Exercises
Literature
Chapter 6. The Postman's Problem
6.1. Introduction
6.2. Postman problem for undirected graph
0.3. Postman Problem for Directed Graph
6.4. Postman problem for mixed graph
Exercises
Literature
Chapter 7. The Traveling Salesman Problem
7.1. Formulation and some properties of the solution to the traveling salesman problem
7.2. Conditions for the existence of a Hamiltonian contour
7.3. Lower bounds
7.4. Methods for Solving the Traveling Salesman Problem
Exercises
Literature
Chapter 8. Hosting Tasks
8.1. Introduction
8.2. Center search tasks
8.3. Median Search Tasks
8.4. Generalizations
Exercises
Literature
Chapter 9. Network Graphics
9.1. Critical path method (MCP)
9.2- Determination of the duration of the execution of "operations from the condition of ensuring the minimum cost
9.3. Generalized network diagrams
Exercises
Literature
Subject index
2012-07-26 at 12:49
 |
Melikhov A.N., Bershtein L.S., Kureichik V.M. The use of graphs for the design of discrete devices - M.: Nauka, 1974, 304 p. |
Content
Foreword
Introduction
Chapter I. Basic definitions and concepts of graph theory
§ 1. Methods of assignment, basic types and parts of graphs
§ 2. Connected graphs
§ 3. Basic numbers of graphs
§ 4. Metric of graphs
§ 5. Planar graphs
§ 6. Isomorphism and isomorphic embedding of graphs
§ 7. Transition from modular schemes to graphs
§ 8. The branch and bound method
Chapter II. Layout of discrete device circuit elements
§ 1. Covering functional diagrams by the module connection diagram
§ 2. Statement of the problem of cutting a circuit graph
§ 3. Sequential cutting algorithms
§ 4. Iterative cutting algorithms
§ 5. Cutting the circuit graph into an arbitrary number of parts
Chapter III. Placing a schematic graph on a plane
§ 1. Statement of the module placement problem
§ 2. Sequential placement algorithms
§ 3. Iterative allocation algorithms
§ 4. Algorithm for placing elements by the branch and bound method
Chapter IV. Minimizing In-Circuit Intersections for Discrete Devices
§ 1. On the number of intersections of edges of complete and cubic graphs
§ 2. Counting the intersections of the edges of arbitrary graphs with a fixed location of the vertices on the plane
§ 3. Counting the intersections of the edges of arbitrary graphs when mapped to a rectangular lattice
§ 4. Minimization of the number of intersections of the edges of the graph of a circuit
Chapter V. Some questions of planarity of graphs of schemes
§ 1. Methods for determining the planarity of a graph
§ 2. On the planarity number of a graph
§ 3. An algorithm for determining the planarity of a graph having a Hamiltonian cycle
§ 4. Partitioning a graph into flat subgraphs
§ 5. Partitioning a graph into flat suraphs using internally stable sets
Chapter VI. Tracing connections of discrete device circuits
§ 1. Statement of the tracing problem
§ 2. Ray tracing algorithms
§ 3. Trace algorithms using the construction of a forest of connecting trees
§ 4. Tracing connections in multiple layers
Bibliography
Name index
Subject index
2012-07-26 at 12:53
 |
Melnikov O.I. Graph theory in entertaining problems. Ed. 3, rev. and add. 2009.232 s. |
Content
Introduction 5
Conditional division of tasks by degrees of complexity 7
Tasks. Problem solutions 8
Used literature 226
Appendix 227
2012-07-26 at 12:57
 |
Ore O. Graphs and their application: Per. from English. 1965.176 s. |
Content
From the editor
Introduction
CHAPTER I. What is a graph?
1. Sports
2. Null graph and complete graph
3. Isomorphic graphs
4. Plane graphs
5. One problem about plane graphs
6. Number of graph edges
CHAPTER II. Connected graphs
1. Components
2. The problem of the Konigsberg bridges
3. Euler graphs
4. Finding the right path
5. Hamiltonian lines
6. Puzzles and graphs
CHAPTER III. Trees
1. Trees and forests
2. Cycles and trees
3. The problem of connecting cities
4. Streets and squares
CHAPTER IV. Establishing correspondences
1. The problem of appointment to positions
2. Other formulations
3. Circular matches
CHAPTER V. Directed Graphs
1. Sports again
2. One-way traffic
3. Degrees of vertices
4. Genealogical graphs
CHAPTER VI. Games and puzzles
1. Puzzles and directed graphs
2. Game theory
3. The sports commentator paradox
CHAPTER VII. Relations
1. Relationships and graphs
2. Special conditions
3. Equivalence relations
4. Partial ordering
CHAPTER VIII. Plane graphs
1. Conditions for plane graphs
2. Euler's formula
3. Some relations for graphs. Dual graphs
4. Regular polyhedra
5. Mosaics
CHAPTER IX, Card Coloring
1. The problem of four colors
2. The five-color theorem
Exercise solutions
Literature
Glossary of key terms used in the book
2012-07-26 at 12:58
 |
Ore O. Theory of graphs. - 2nd ed. - M .: Nauka, Main edition of physical and mathematical literature, 1980, 336 p. |
Content
From the editor of the Russian translation 8
Foreword 9
Chapter 1. BASIC CONCEPTS 11
1.1. Definitions 11
1.2. Local degrees 16
1.3. Parts and Subgraphs 22
1.4. Binary Relations 25
1.5. Adjacency n Incidence Matrices 30
Chapter 2. CONNECTIVITY 34
2.1. Routes, chains and simple chains 34
2.2. Connected components 36
2.3. One-to-One Mappings 39
2.4. Distances 41
2.5. Length 45
2.6. Matrices and chains. Product of graphs 43
2.7. Puzzle 51
Chapter 3. CHAIN \u200b\u200bPROBLEMS 53
3.1. Euler chains 53
3.2. Euler chains in infinite graphs 58
3.3. About mazes 64
3.4. Hamiltonian cycles 70
Chapter 4. TREES 77
4.1. Properties of trees 77
4.2. Centers in the trees 82
4.3. Cyclic rank (diplomatic number) 87
4.4. Single-valued mappings 88
4.5. Freely Drawn Boxes 96
Chapter 5. SHEETS AND BLOCKS 101
5.1. Connecting edges and vertices 101
5.2. Sheets 105
5.3. Homomorphic Images of a Graph 107
5.4. Blocks 109
5.5. Maximum Simple Cycles 114
Chapter 6. AXIOM OF CHOICE 117
6.1. Complete order 117
6.2. Maximum Principles 120
6.3. Chain-Sum Properties 123
6.4. Maximum exception columns 126
6.5. Maximum trees 128
6.6. Relations between the maximum graphs 130
Chapter 7. THEOREMS ON PAIRS 134
7.1. Bipartite graphs 134
7.2. Deficits 138
7.3. Matching Theorems 141
7.4. Reciprocal Matchings 145
7.5. Matching in graphs of particular type 150
7.6. Bipartite graphs with positive 155
7.7. Applications to matrices 160
7.8. Alternating chains and max 167
7.9. Separating Sets 176
7.10. Combined matchings 178
Chapter 8. ORIENTED GRAPHS 184
8.1. Inclusion ratio and achievable 184
8.2. Homomorphism theorem 189
8.3. Transitive graphs and immersions in ordering relations 191
8.4. Basis Graphs 194
8.5. Alternating chains 198
8.6. Sugrafs of the first degree in box 202
Chapter 9. ACYCLIC GRAPHS 206
9.1. Basis Graphs 206
9.2. Chain deformations 208
9.3. Reproduction graphs 211
Chapter 10. PARTIAL ORDER 216
10.1. Partial Ordering Graphs 216
10.2. Sums of Ordered Sets 217
10.3. Structures and structural operations. Closure Relationships 223
10.4. Dimension in Partial Ordering 227
Chapter 11. BINARY RELATIONS AND GALOIS RELATIONS 232
11.1. Galois matches 232
11.2. Galois Links for Binary Relations 237
11.3. Alternating work relationship 242
11.4. Ferrers' Relationship 245
Chapter 12. BONDING CHAINS 248
12.1. The secant chain theorem 248
12.2. Vertex division 252
12.3. Rib separation 254
12.4. Deficit 256
Chapter 13. DOMINANT SETS COVERING 260
SETS AND INDEPENDENT SETS
13.1. Dominant sets 260
13.2. Covering Sets and Covering 262
13.3. Independent Sets 266
13.4. Turan's Theorem 270
13.5. Ramsey's theorem 273
13.6. One problem from information theory
Chapter 14. CHROMATIC GRAPHS
14.1. Chromatic number
14.2. Sums of chromatic graphs
14.3. Critical graphs
14.4. Coloring polynomials
Chapter 15. GROUPS AND GRAPHS
15.1. Automorphism groups
15.2. Colored Cayley graphs for groups
15.3. Graphs with given groups
15.4. Edge mappings
Literature
Name index
Subject index
2012-07-26 at 12:58
Content
Translation Editor's Foreword
Foreword
Part I. Graph theory
1. Basic concepts
1.1. Basic definitions
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Exercises
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Exercises
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Exercises
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Exercises
Literature
Subject index
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Content
Translation Editor's Foreword
Foreword
1. Introduction
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Bibliography
Subject index
Download (djvu, 4 Mb) libgen.info
Content
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Content
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Electrical circuits
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{!LANG-965279b5798ce76fa7396a09fe7900d0!}
The four-color hypothesis
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Graph types
Routes and connectivity
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Ramsey problem
Extreme graphs
Intersection graphs
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Exercises
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Articulation points, bridges and blocks
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Exercises
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Description of trees
Centers and centroids
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Matroids
Exercises
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Connectivity and edge connectivity
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Other variants of Menger's theorem 70
Exercises 74
Chapter 6. Partitions 76
Exercises 81
Chapter 7. Traversing Graphs 83
Euler Graphs 83
Hamiltonian graphs 85
Exercises 88
Chapter 8. Edge graphs 91
Some properties of edge graphs 91
Characterization of edge graphs 94
Special edge graphs 99
Edge graphs and traversals 101
Total Counts 103
Exercises 104
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Exercises 116
Chapter 10. Coatings 117
Covers and independence 117
Critical vertices and edges 120
Costal nucleus 122
Exercises 124
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Outerplanar graphs 131
The Pontryagin-Kuratovsky theorem 133
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Genus, thickness, size, number of crosses 141
Exercises 148
Chapter 12. Coloring Pages 151
Chromatic number 152
Five-color theorem 155
The four-color hypothesis 156
Hewood Card Coloring Theorem 162
Uniquely Colorable Graphs 164
Critical columns 167
Homomorphisms 169
Chromatic polynomial 172
Exercises 175
Chapter 13. Matrices 178
Adjacency Matrix 178
Incident Matrix 180
Loop Matrix 183
Overview of additional properties of matroids 186
Exercises 187
Chapter 14. Groups 189
The group of automorphisms of a graph 193
Operations on Substitution Groups 194
Graph composition group 195
Counts with this group 198
Symmetric graphs 201
Stronger Symmetry Graphs 204
Exercises 206
Chapter 15. Enumerations 209
Marked boxes 209
Polya's enumeration theorem 211
Enumeration of columns 216
Tree listing 219
Enumeration theorem for a power group 224
Solved and Unsolved Graph Enumeration Problems 225
Exercises 230
Chapter 16. Digraphs 232
Digraphs and Connectivity 232
Oriented duality and contourless digraphs 234
Digraphs and Matrices 237
Overview on Tournament Recovery 244
Exercises 244
Appendix I. Graph diagrams 248
Appendix II. Digraph Charts 260
Appendix III. Tree diagrams 266
References and index 268
Symbol Index 291
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 |
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Content
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Translation Editor's Foreword |
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Introduction |
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{!LANG-77c15e513476957c72757df9a33da58c!} |
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Königsberg bridges problem |
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Chemical isomers |
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{!LANG-042e2e475bf6bfa6ec2bbd96865c8411!} |
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Graph theory in the twentieth century |
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{!LANG-94095252b7e25fde63b470963f56406c!} |
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Graph operations |
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Exercises |
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{!LANG-356bd69525dafe3873ea212f2df61cec!} |
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{!LANG-ba652ad743589171e6d3567c13f44a3d!} |
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Block graphs and articulation point graphs |
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Exercises |
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{!LANG-ef09e3b931559525ae16443e9f1c54ce!} |
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{!LANG-7101dbbf0b8064a20bf9c4a8072fcd18!} |
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Block and articulation trees |
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Independent cycles and cocycles |
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{!LANG-7d6c5510ac2233157a53c4472d432df8!} |
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Exercises |
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{!LANG-f8886fb0a20801d402a892e5eaeda6f7!} |
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{!LANG-f5642deb1dec3a35a8afa6e9f1aac4aa!} |
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Graphic variants of Menger's theorem |
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Other variants of Menger's theorem |
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Exercises |
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{!LANG-ec3b54dfe4d2ac8bbbf9979e59955e1e!} |
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Exercises |
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{!LANG-4fe82eab03d80167230cae831ae9c58d!} |
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Exercises |
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Some properties of edge graphs |
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Edge graphs and traversals |
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Exercises |
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Exercises |
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{!LANG-e32cc0b84c94b46cd8dd01c92ecb4912!} |
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Critical vertices and edges |
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Exercises |
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{!LANG-a59899145dcabd95f64e7d04e66184f1!} |
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The Pontryagin - Kuratovsky theorem |
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Genus, thickness, size, number of crosses |
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Exercises |
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The five-color theorem |
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Uniquely Colorable Graphs |
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Exercises |
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Adjacency matrix |
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Incident matrix |
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Exercises |
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Operations on substitution groups |
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Stronger Symmetry Graphs |
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Exercises |
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Labeled graphs |
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Exercises |
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Oriented duality and contourless digraphs |
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{!LANG-23ac84d50404aac9c45d142b44c4cd7e!} |
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Exercises |
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{!LANG-c036f337b6aecbd18945ee1c13dc76fe!} |
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References and index |
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Subject index |
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Subject index |
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