Matroid theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Edition: | 2. ed. |
| Series: | Oxford graduate texts in mathematics
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 684 Seiten Illustrationen, Diagramme |
| ISBN: | 9780199603398 9780198566946 |
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Record in the Search Index
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| adam_text |
Titel: Matroid theory
Autor: Oxley, James G
Jahr: 2011
Preliminaries
1 Basic definitions and examples
1.1 Independent sets and circuits
1.2 Bases
1.3 Rank
1.4 Closure
1.5 Geometrie representations of matroids of small rank
1.6 Transversal matroids
1.7 The lattice of flats
1.8 The greedy algorithm
CONTENTS
7
7
15
20
25
32
43
48
58
Duality 64
2.1 The definition and basic properties 64
2.2 Duals of representable matroids 77
2.3 Duals of graphic matroids 87
2.4 Duals of transversal matroids 93
Minors 100
3.1 Contraction 100
3.2 Minors of certain classes of matroids 106
3.3 The Scum Theorem, projeetion, and flats 113
Connectivity 118
4.1 Connectivity for graphs and matroids 118
4.2 Properties of matroid Connectivity 122
4.3 More properties of Connectivity 126
Graphic matroids 135
5.1 Representability 135
5.2 Duality in graphic matroids 140
5.3 Whitney's 2-Isomorphism Theorem 145
5.4 Series-parallel networks 151
Representable matroids 158
6.1 Projective geometries 159
6.2 Affine geometries *'"
6.3 Different matroid representations 176
6.4 Constructing representations for matroids 181
6.5 Representability over finite fields 192
6.6 Regulär matroids 204
6.7 Algebraic matroids 211
xii Contents
6.8 Characteristic sets and decidability 220
6.9 Moduiarity 228
6.10 Dowling geometries 235
7 Constructions 251
7.1 Series and parallel connection and 2-sums 251
7.2 Single-elernent extensions 264
7.3 Quotients and related Operations 272
7.4 A non-commutative Operation 282
8 Higher Connectivity 291
8.1 Tutte's defmition 291
8.2 Properties of the Connectivity function 296
8.3 3-connected matroids and 2-sums 304
8.4 Wheels and whirls 316
8.5 Tutte's Linking Theorem and its applications 319
8.6 Matroid versus graph Connectivity 324
8.7 Some extremal Connectivity results 332
8.8 Tutte's Wheels-and-Whirls Theorem 337
9 Binary matroids 344
9.1 Characterizations 344
9.2 Circuit and cocircuit Spaces 349
9.3 The Operation of 3-sum 353
9.4 Other special properties 360
10 Excluded-minor theorems 372
10.1 The characterization of regulär matroids 372
10.2 The characterization of ternary matroids 380
10.3 The characterization of graphic matroids 385
10.4 Further properties of regulär and graphic matroids 398
11 Submodular functions and matroid imion 404
11.1 Deriving matroids from submodular functions 404
11.2 The theorems of Hall and Rado 411
11.3 Matroid union and its applications 427
11.4 Amalgams and the generalized parallel connection 436
11.5 Generalizations of delta-wye exchange 448
12 The Splitter Theorem 457
12.1 The theorem and its proof 457
12.2 Applications of the Splitter Theorem 465
12.3 Variations on the Splitter Theorem 477
13 Seymour's Decomposition Theorem 489
13.1 Overview 489
13.2 Graphic, cographic, or a special minor 494
Contents xiii
13.3 Blocking sequences 507
13.4 J?i2-minors 517
14 Research in representability and structure 525
14.1 The Well-Quasi-Ordering Conjecture for Matroids 525
14.2 Branch-width 529
14.3 Rota's Conjecture and the Well-Quasi-Ordering Conjecture 536
14.4 Algorithmic consequences 540
14.5 Intertwining 543
14.6 Inequivalent representations 550
14.7 Ternary matroids 555
14.8 Stabilizers 561
14.9 Unavoidable minors 569
14.10 Growth rates 570
15 Unsolved problems 583
15.1 Representability: linear and algebraic 584
15.2 Unimodal conjectures 585
15.3 Critical problems 588
15.4 From graphs to matroids 591
15.5 Enumeration 593
15.6 Gammoids and transversal matroids 598
15.7 Excluding a uniform matroid 599
15.8 Negative correlation 600
15.9 A miscellany 604
References 608
Appendix: Some interesting matroids 639
List of tables 665
Notation 666
Index 668 |
| any_adam_object | 1 |
| author | Oxley, James G. 1953- |
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 9780199603398 9780198566946 |
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| physical | XIII, 684 Seiten Illustrationen, Diagramme |
| publishDate | 2011 |
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| spelling | Oxley, James G. 1953- Verfasser (DE-588)143773488 aut Matroid theory James Oxley 2. ed. Oxford [u.a.] Oxford Univ. Press 2011 XIII, 684 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 21 Matroid (DE-588)4128705-8 gnd rswk-swf Matroidtheorie (DE-588)4446429-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Matroid (DE-588)4128705-8 s Matroidtheorie (DE-588)4446429-0 s DE-604 Oxford graduate texts in mathematics 21 (DE-604)BV011416591 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021181132&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 | Oxley, James G. 1953- Matroid theory Oxford graduate texts in mathematics Matroid (DE-588)4128705-8 gnd Matroidtheorie (DE-588)4446429-0 gnd |
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| title | Matroid theory |
| title_auth | Matroid theory |
| title_exact_search | Matroid theory |
| title_full | Matroid theory James Oxley |
| title_fullStr | Matroid theory James Oxley |
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| topic_facet | Matroid Matroidtheorie Lehrbuch |
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