Circuit double cover of graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2012
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society lecture note series
399 |
| Schlagworte: | |
| Online-Zugang: | http://scans.hebis.de/HEBCGI/show.pl?29256589_toc.html http://scans.hebis.de/HEBCGI/show.pl?29256589_kub.html http://scans.hebis.de/HEBCGI/show.pl?29256589_aub.html http://scans.hebis.de/HEBCGI/show.pl?29256589_bio.html Inhaltsverzeichnis |
| Beschreibung: | XXI, 357 S. graph. Darst. 23x15 cm |
| ISBN: | 9780521282352 0521282357 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804149082539687936 |
|---|---|
| adam_text | Titel: Circuit double cover of graphs
Autor: Zhang, Cun-Quan
Jahr: 2012
Contents
Foreword (by Brian Alspach) poge xiii
Foreword (by Michael Tarsi) xv
Preface xix
Circuit double cover 1
1.1 Circuit double cover conjecture 2
1.2 Minimal counterexamples 3
1.3 3-edge-coloring and even subgraph cover 5
1.4 Circuit double Covers and graph embeddings 6
1.5 Open problems 8
1.6 Exercises 8
Faithful circuit cover 10
2.1 Faithful circuit cover 10
2.2 3-edge-coloring and faithful cover 13
2.3 Construction of contra pairs 14
2.4 Open problems 18
2.5 Exercises 19
Circuit chain and Petersen minor 21
3.1 Weight decomposition and removable circuit 21
3.2 Cubic minimal contra pair 22
3.3 Minimal contra pair 25
3.4 Structure of circuit chain 28
3.5 Open problems 31
3.6 Exercises 31
Small oddness 35
4.1 it-even subgraph double covers 35
4.2 Small oddness 37
viii Contents
4.3 Open problems 43
4.4 Exercises 44
5 Spanning minor, Kotzig frames 45
5.1 Spanning Kotzig subgraphs 45
5.2 Kotzig frames 51
5.3 Construction of Kotzig graphs 56
5.4 Three-Hamilton circuit double Covers 58
5.5 Open problems 61
5.6 Exercises 63
6 Strong circuit double cover 66
6.1 Circuit extension and strong CDC 66
6.2 Thomason s lollipop method 67
6.3 Stable circuits 70
6.4 Extension-inheritable properties 71
6.5 Extendable circuits 74
6.6 Semi-extension of circuits 76
6.7 Circumferences 79
6.8 Open problems 80
6.9 Exercises 81
7 Spanning trees, supereulerian graphs 83
7.1 Jaeger Theorem: 2-even subgraph covers 83
7.2 Jaeger Theorem: 3-even subgraph covers 85
7.3 Even subgraph 2fc-covers 87
7.4 Catlin s collapsible graphs 89
7.5 Exercises 93
8 Flows and circuit covers 96
8.1 Jaeger Theorems: 4-flow and 8-flow 96
8.2 4-flows 97
8.3 Seymour Theorem: 6-flow 101
8.4 Contractible configurations for 4-flow 104
8.5 Bipartizing matching, flow covering 105
8.6 Exercises 108
9 Girth, embedding, small cover 112
9.1 Girth 112
9.2 Small genus embedding 112
9.3 Small circuit double covers 115
9.4 Exercises 116
Contents ix
10 Compatible circuit decompositions 117
10.1 Introduction 117
10.2 Relation with faithful circuit cover 118
10.3 Counterexamples and graph minor related results 121
10.4 Planar graphs 122
10.5 Dominating circuit and Sabidussi Conjecture 125
10.6 Construction of contra pairs 126
10.7 Open problems 130
10.8 Exercises 131
11 Other circuit decompositions 134
11.1 Restricted circuit decompositions 134
11.2 Open problems 136
11.3 Exercises 136
12 Reductions of weights, coverages 137
12.1 Weight reduction for contra pairs 137
12.2 Coverage reduction with fixed parity 150
12.3 Exercises 151
13 Orientable cover 153
13.1 Orientable double cover 153
13.2 Circular double covers and modulo orientations 157
13.3 Open problems 161
13.4 Exercises 162
14 Shortest cycle covers 163
14.1 Shortest cover and double cover 163
14.2 Minimum eulerian weight 166
14.3 3-even subgraph covers 168
14.3.1 Basis of cycle space 168
14.3.2 3-even subgraph covers 169
14.3.3 ( 4)-even subgraph covers 171
14.3.4 Upper bounds of SCC3 171
14.3.5 Relations with other major conjectures 172
14.3.6 Fano plane and Fano flows 174
14.3.7 Incomplete Fano flows, F^-flows 179
14.3.8 Someproofs 182
14.4 Open problems 186
14.5 Exercises 187
15 Beyond integer (1,2)-weight 189
15.1 Rational weights 190
x Contents
15.2 Group weights 193
15.3 Integer weights 194
15.3.1 Non-negative weights and Petersen minor 194
15.3.2 Integer semi-group weights 194
15.3.3 Small ränge 195
15.4 Open problems 197
15.5 Exercises 197
16 Petersen chain and Hamilton weights 199
16.1 Local structures 200
16.2 Hamilton weight 202
16.3 (/C4)-graphs 204
16.4 Pio-free Hamilton weighted graphs 212
16.5 Circuit chain and Petersen chain 216
16.6 Minimal contra pair 237
16.7 Open problems 238
16.8 Exercises 239
Appendix A Preliminary 243
A.l Fundamental theorems 243
A.2 Even subgraphs and parity subgraphs 247
A.3 Exercises 250
Appendix B Snarks, Petersen graph 252
B.l 3-edge-coloring of cubic graphs, snarks 252
B.l.l Parity lemma 253
B.1.2 Snarks 253
B.1.3 Construction of snarks 254
B.1.4 Girths and bonds of snarks 256
B.1.5 Small snarks 258
B.2 A mini encyclopedia of the Petersen graph 260
B.3 Exercises 268
B.4 Various drawings of the Petersen graph 269
Appendix C Integer flow theory 273
C.l Tutte s integer flows 273
C.2 Fundamental lemmas 277
C.3 Exercises 279
Appendix D Hints for exercises 285
Contents xi
Glossary of terms and Symbols 322
References 337
Author index 351
Subject index 354
|
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| dewey-raw | 511.5 |
| dewey-search | 511.5 |
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| discipline | Mathematik |
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| isbn | 9780521282352 0521282357 |
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| spelling | Zhang, Cun-Quan Verfasser aut Circuit double cover of graphs Cun-Quan Zhang 1. publ. Cambridge Cambridge Univ. Press 2012 XXI, 357 S. graph. Darst. 23x15 cm txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 399 Überdeckung Mathematik (DE-588)4186551-0 gnd rswk-swf Zusammenhängender Graph (DE-588)4251368-6 gnd rswk-swf Überdeckung Mathematik (DE-588)4186551-0 s Zusammenhängender Graph (DE-588)4251368-6 s DE-604 London Mathematical Society lecture note series 399 (DE-604)BV000000130 399 X:Nielsen text/html http://scans.hebis.de/HEBCGI/show.pl?29256589_toc.html X:Nielsen text/html http://scans.hebis.de/HEBCGI/show.pl?29256589_kub.html X:Nielsen text/html http://scans.hebis.de/HEBCGI/show.pl?29256589_aub.html X:Nielsen text/html http://scans.hebis.de/HEBCGI/show.pl?29256589_bio.html HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024978379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Circuit double cover of graphs |
| title_auth | Circuit double cover of graphs |
| title_exact_search | Circuit double cover of graphs |
| title_full | Circuit double cover of graphs Cun-Quan Zhang |
| title_fullStr | Circuit double cover of graphs Cun-Quan Zhang |
| title_full_unstemmed | Circuit double cover of graphs Cun-Quan Zhang |
| title_short | Circuit double cover of graphs |
| title_sort | circuit double cover of graphs |
| topic | Überdeckung Mathematik (DE-588)4186551-0 gnd Zusammenhängender Graph (DE-588)4251368-6 gnd |
| topic_facet | Überdeckung Mathematik Zusammenhängender Graph |
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