Graphs and hypergraphs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam (u.a.)
North-Holland Publ. Co. (u.a.)
1976
|
| Edition: | 2., rev. ed. |
| Series: | North-Holland mathematical library.
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 528 S. graph.Darst. |
| ISBN: | 0720424534 |
Staff View
MARC
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| 264 | 1 | |a Amsterdam (u.a.) |b North-Holland Publ. Co. (u.a.) |c 1976 | |
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Record in the Search Index
| _version_ | 1804116428623708160 |
|---|---|
| adam_text | TABLE OF CONTENTS
PART ONE—GRAPHS
CHAPTER 1. BASIC CONCEPTS
1. Graphs 3
2. Basic definitions 5
3. List of symbols 9
CHAPTER 2. CYCLOMATIC NUMBER
1. Cycles and cocycles 12
2. Cycles in a planar graph 17
CHAPTER 3. TREES AND ARBORESCENCES
1. Trees and cotrees 24
2. Strongly connected graphs and graphs without circuits .... 28
3. Arborescences 32
4. Injective, functional and semi functional graphs 36
5. Counting trees 42
CHAPTER 4. PATHS, CENTRES AND DIAMETERS
1. The path problem 55
2. The shortest path problem 59
3. Centres and radii of a quasi strong!/ connected graph 61
4. Diameter of a strongly connected graph 66
5. Counting paths 74
CHAPTER 5. FLOW PROBLEMS
1. The maximum flow problem 76
2. The compatible flow problem 86
3. An algebraic study of flows and tensions 89
4. The maximum tension problem 95
CHAPTER 6. DEGREES AND DEMI DEGREES
1. Existence of a p graph with given demi degrees 102
2. Existence of a p graph without loops with given demi degrees . .109
3. Existence of a simple graph with given degrees 115
xi
Xii TABLE OF CONTENTS
CHAPTER 7. MATCHINGS
1. The maximum matching problem 122
2. The minimum covering problem 129
3. Matchings in bipartite graphs 131
4. An extension of the Konig theorem 141
5. Counting perfect matchings 142
CHAPTER 8. c MATCHINGS
1. The maximum c matching problem 150
2. Transfers 153
3. Maximum cardinality of a c matching 155
CHAPTER 9. CONNECTIVITY
1. /( Connected graphs 164
2. Articulation vertices and blocks 175
3. ^ Edge connected graphs 181
CHAPTER 10. HAMILTONIAN CYCLES
1. Hamiltonian paths and circuits 186
2. Hamiltonian paths in complete graphs 192
3. Existence theorems for hamiltonian circuits 195
4. Existence theorems for hamiltonian cycles 204
5. Hamilton connected graphs 217
6. Hamiltonian cycles in planar graphs (abstract) 223
CHAPTER 11. COVERING EDGES WITH CHAINS
1. Eulerian cycles 228
2. Covering edges with disjoint chains 232
3. Counting eulerian circuits 239
CHAPTER 12. CHROMATIC INDEX
1. Edge colourings 248
2. The Vizing theorem and related results 254
3. Edge colourings of planar graphs (abstract) 267
TABLE OF CONTENTS xiii
CHAPTER 13. STABILITY NUMBER
1. Maximum stable sets 272
2. The Turan theorem and related results 278
3. a Critical graphs 285
4. Critical vertices and critical edges 297
5. Stability number and vertex coverings by paths 298
CHAPTER 14. KERNELS AND GRUNDY FUNCTIONS
1. Absorption number 303
2. Kernels 307
3. Grundy functions 312
4. Nim games 318
CHAPTER 15. CHROMATIC NUMBER
1. Vertex colourings 325
2. y Critical graphs 338
3. The Hajos theorem 350
4. Chromatic polynomials 352
5. Vertex colourings of planar graphs (abstract) 355
CHAPTER 16. PERFECT GRAPHS
1. Perfect graphs 360
2. Comparability graphs 363
3. Triangulated graphs 368
4. i Triangulated graphs 369
5. Interval graphs 371
6. Cartesian product and Cartesian sum of simple graphs .... 376
PART TWO—HYPERGRAPHS
CHAPTER 17. HYPERGRAPHS AND THEIR DUALS
1. Hypergraphs 389
2. Cycles in a hypergraph 391
3. Conformal hypergraphs 396
4. Representative graph of a hypergraph 400
CHAPTER 18. TRANSVERSALS
1. Matchings and c matchings 414
2. Transversal number 420
XIV TABLE OF CONTENTS
CHAPTER 19. CHROMATIC NUMBER OF A HYPERGRAPH
1. Stability number and chromatic number of a hypergraph .... 428
2. Cliques of a hypergraph 432
3. Good colourings of the edges of a graph 440
4. Generalizations of the chromatic number of a graph 443
CHAPTER 20. BALANCED HYPERGRAPHS AND UNIMODULAR
HYPERGRAPHS
1. Strong chromatic number 448
2. Balanced hypergraphs 450
3. Unimodular hypergraphs 463
4. Stochastic functions 469
CHAPTER 21. MATROIDS
1. Matroid on a set 476
2. The Rado theorem and related results 481
3. Image of a matroid 486
4. Minimum weight basis 493
REFERENCES 498
INDEX OF DEFINITIONS 523
|
| any_adam_object | 1 |
| author | Berge, Claude 1926-2002 |
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| ctrlnum | (OCoLC)2107701 (DE-599)BVBBV001983162 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2., rev. ed. |
| format | Book |
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| id | DE-604.BV001983162 |
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| indexdate | 2024-07-09T15:38:21Z |
| institution | BVB |
| isbn | 0720424534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001293509 |
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| physical | XIV, 528 S. graph.Darst. |
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| publishDate | 1976 |
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| publisher | North-Holland Publ. Co. (u.a.) |
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| series | North-Holland mathematical library. |
| series2 | North-Holland mathematical library. |
| spelling | Berge, Claude 1926-2002 Verfasser (DE-588)107792109 aut Graphes et hypergraphes Graphs and hypergraphs 2., rev. ed. Amsterdam (u.a.) North-Holland Publ. Co. (u.a.) 1976 XIV, 528 S. graph.Darst. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library. 6 Grafentheorie gtt Graphes, Théorie des Hypergraphes Graph theory Hypergraphs Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Hypergraph (DE-588)4161063-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Graph (DE-588)4021842-9 s DE-604 Hypergraph (DE-588)4161063-5 s Graphentheorie (DE-588)4113782-6 s 2\p DE-604 North-Holland mathematical library. 6 (DE-604)BV000005206 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001293509&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berge, Claude 1926-2002 Graphs and hypergraphs North-Holland mathematical library. Grafentheorie gtt Graphes, Théorie des Hypergraphes Graph theory Hypergraphs Graphentheorie (DE-588)4113782-6 gnd Graph (DE-588)4021842-9 gnd Hypergraph (DE-588)4161063-5 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4021842-9 (DE-588)4161063-5 (DE-588)4151278-9 |
| title | Graphs and hypergraphs |
| title_alt | Graphes et hypergraphes |
| title_auth | Graphs and hypergraphs |
| title_exact_search | Graphs and hypergraphs |
| title_full | Graphs and hypergraphs |
| title_fullStr | Graphs and hypergraphs |
| title_full_unstemmed | Graphs and hypergraphs |
| title_short | Graphs and hypergraphs |
| title_sort | graphs and hypergraphs |
| topic | Grafentheorie gtt Graphes, Théorie des Hypergraphes Graph theory Hypergraphs Graphentheorie (DE-588)4113782-6 gnd Graph (DE-588)4021842-9 gnd Hypergraph (DE-588)4161063-5 gnd |
| topic_facet | Grafentheorie Graphes, Théorie des Hypergraphes Graph theory Hypergraphs Graphentheorie Graph Hypergraph Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001293509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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