Introduction to graph theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Prentice Hall
2001
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 588 S. graph. Darst. |
| ISBN: | 0130144002 |
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| 245 | 1 | 0 | |a Introduction to graph theory |c Douglas B. West |
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Record in the Search Index
| _version_ | 1804128253935353856 |
|---|---|
| adam_text | Titel: Introduction to graph theory
Autor: West, Douglas Brent
Jahr: 2001
Contents
Preface xi
Chapter 1 Fundamental Concepts 1
1.1 What Is a Graph? 1
The Definition, 1
Graphs as Models, 3
Matrices and Isomorphism, 6
Decomposition and Special Graphs, 11
Exercises, 14
1.2 Paths, Cycles, and Trails 19
Connection in Graphs, 20
Bipartite Graphs, 24
Eulerian Circuits, 26
Exercises, 31
1.3 Vertex Degrees and Counting 34
Counting and Bijections, 35
Extremal Problems, 38
Graphic Sequences, 44
Exercises, 47
1.4 Directed Graphs 53
Definitions and Examples, 53
Vertex Degrees, 58
Eulerian Digraphs, 60
Orientations and Tournaments, 61
Exercises, 63
v
vi Contents
Chapter 2 Trees and Distance 67
2.1 Basic Properties 67
Properties of Trees, 68
Distance in Trees and Graphs, 70
Disjoint Spanning Trees (optional), 73
Exercises, 75
2.2 Spanning Trees and Enumeration 81
Enumeration of Trees, 81
Spanning Trees in Graphs, 83
Decomposition and Graceful Labelings, 87
Branchings and Eulerian Digraphs (optional), 89
Exercises, 92
2.3 Optimization and Trees 95
Minimum Spanning Tree, 95
Shortest Paths, 97
Trees in Computer Science (optional), 100
Exercises, 103
Chapter 3 Matchings and Factors 107
3.1 Matchings and Covers 107
Maximum Matchings, 108
Hall s Matching Condition, 110
Min-Max Theorems, 112
Independent Sets and Covers, 113
Dominating Sets (optional), 116
Exercises, 118
3.2 Algorithms and Applications 123
Maximum Bipartite Matching, 123
Weighted Bipartite Matching, 125
Stable Matchings (optional), 130
Faster Bipartite Matching (optional), 132
Exercises, 134
3.3 Matchings in General Graphs 136
Tutte s 1-factor Theorem, 136
/-factors of Graphs (optional), 140
Edmonds Blossom Algorithm (optional), 142
Exercises, 145
Contents vii
Chapter 4 Connectivity and Paths 149
4.1 Cuts and Connectivity 149
Connectivity, 149
Edge-connectivity, 152
Blocks, 155
Exercises, 158
4.2 A connected Graphs 161
2-connected Graphs, 161
Connectivity of Digraphs, 164
^-connected and fc-edge-connected Graphs, 166
Applications of Menger s Theorem, 170
Exercises, 172
4.3 Network Flow Problems 176
Maximum Network Flow, 176
Integral Plows, 181
Supplies and Demands (optional), 184
Exercises, 188
Chapter 5 Coloring of Graphs 191
5.1 Vertex Colorings and Upper Bounds 191
Definitions and Examples, 191
Upper Bounds, 194
Brooks Theorem, 197
Exercises, 199
5.2 Structure of Achromatic Graphs 204
Graphs with Large Chromatic Number, 205
Extremal Problems and Turan s Theorem 207
Color-Critical Graphs, 210
Forced Subdivisions, 212
Exercises, 214
5.3 Enumerative Aspects 219
Counting Proper Colorings, 219
Chordal Graphs, 224
A Hint of Perfect Graphs, 226
Counting Acyclic Orientations (optional), 228
Exercises, 229
viii Contents
Chapter 6 Planar Graphs 233
6.1 Embeddings and Euler s Formula 233
Drawings in the Plane, 233
Dual Graphs, 236
Euler s Formula, 241 255
Exercises, 243
6.2 Characterization of Planar Graphs 246
Preparation for Kuratowski s Theorem, 247
Convex Embeddings, 248
Planarity Testing (optional), 252
Exercises, 255
6.3 Parameters of Planarity 257
Coloring of Planar Graphs, 257
Crossing Number, 261
Surfaces of Higher Genus (optional), 266
Exercises, 269
Chapter 7 Edges and Cycles 273
7.1 Line Graphs and Edge-coloring 273
Edge-colorings, 274
Characterization of Line Graphs (optional), 279
Exercises, 282
7.2 Hamiltonian Cycles 286
Necessary Conditions, 287
Sufficient Conditions, 288
Cycles in Directed Graphs (optional), 293
Exercises, 294
7.3 Planarity, Coloring, and Cycles 299
Tait s Theorem, 300
Grinberg s Theorem, 302
Snarks (optional), 304
Plows and Cycle Covers (optional), 307
Exercises, 314
Contents ix
Chapter 8 Additional Topics (optional) 319
8.1 Perfect Graphs 319
The Perfect Graph Theorem, 320
Chordal Graphs Revisited, 323
Other Classes of Perfect Graphs, 328
Imperfect Graphs, 334
The Strong Perfect Graph Conjecture, 340
Exercises, 344
8.2 Matroids 349
Hereditary Systems and Examples, 349
Properties of Matroids, 354
The Span Function, 358
The Dual of a Matroid, 360
Matroid Minors and Planar Graphs, 363
Matroid Intersection, 366
Matroid Union, 369
Exercises, 372
8.3 Ramsey Theory 378
The Pigeonhole Principle Revisited, 378
Ramsey s Theorem, 380
Ramsey Numbers, 383
Graph Ramsey Theory, 386
Sperner s Lemma and Bandwidth, 388
Exercises, 392
8.4 More Extremal Problems 396
Encodings of Graphs, 397
Branchings and Gossip, 404
List Coloring and Choosability, 408
Partitions Using Paths and Cycles, 413
Circumference, 416
Exercises, 422
8.5 Random Graphs 425
Existence and Expectation, 426
Properties of Almost All Graphs, 430
Threshold Functions, 432
Evolution and Graph Parameters, 436
Connectivity, Cliques, and Coloring, 439
Martingales, 442
Exercises, 448
x Contents
8.6 Eigenvalues of Graphs 452
The Characteristic Polynomial, 453
Linear Algebra of Real Symmetric Matrices, 456
Eigenvalues and Graph Parameters, 458
Eigenvalues of Regular Graphs, 460
Eigenvalues and Expanders, 463
Strongly Regular Graphs, 464
Exercises, 467
Appendix A Mathematical Background 471
Sets, 471
Quantifiers and Proofs, 475
Induction and Recurrence, 479
Functions, 483
Counting and Binomial Coefficients, 485
Relations, 489
The Pigeonhole Principle, 491
Appendix B Optimization and Complexity 493
Intractability, 493
Heuristics and Bounds, 496
NP-Completeness Proofs, 499
Exercises, 505
Appendix C Hints for Selected Exercises 507
General Discussion, 507
Supplemental Specific Hints, 508
Appendix D Glossary of Terms 515
Appendix E Supplemental Reading 533
Appendix F References 567
Author Index 569
Subject Index 575
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| spelling | West, Douglas Brent Verfasser (DE-588)1157982476 aut Introduction to graph theory Douglas B. West 2. ed. Upper Saddle River, NJ Prentice Hall 2001 XIX, 588 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grafentheorie gtt Graphes, Théorie des TEORIA DOS GRAFOS larpcal Graph theory Graph (DE-588)4021842-9 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Graph (DE-588)4021842-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009188736&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | West, Douglas Brent Introduction to graph theory Grafentheorie gtt Graphes, Théorie des TEORIA DOS GRAFOS larpcal Graph theory Graph (DE-588)4021842-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4113782-6 |
| title | Introduction to graph theory |
| title_auth | Introduction to graph theory |
| title_exact_search | Introduction to graph theory |
| title_full | Introduction to graph theory Douglas B. West |
| title_fullStr | Introduction to graph theory Douglas B. West |
| title_full_unstemmed | Introduction to graph theory Douglas B. West |
| title_short | Introduction to graph theory |
| title_sort | introduction to graph theory |
| topic | Grafentheorie gtt Graphes, Théorie des TEORIA DOS GRAFOS larpcal Graph theory Graph (DE-588)4021842-9 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Grafentheorie Graphes, Théorie des TEORIA DOS GRAFOS Graph theory Graph Graphentheorie |
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