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Circuit Double Cover of Graphs.
Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
|
| Colección: | London Mathematical Society Lecture Note Series, 399.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Zhang, Cun-Quan. | |
| 245 | 1 | 0 | |a Circuit Double Cover of Graphs. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource (381 pages) | ||
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| 490 | 1 | |a London Mathematical Society Lecture Note Series, 399 ; |v v. 399 | |
| 505 | 0 | |a Cover; Series; Title; Copyright; Dedication; Contents; Foreword; Foreword; Preface; 1: Circuit double cover; 1.1 Circuit double cover conjecture; 1.2 Minimal counterexamples; 1.3 3-edge-coloring and even subgraph cover; 1.4 Circuit double covers and graph embeddings; 1.5 Open problems; 1.6 Exercises; 2: Faithful circuit cover; 2.1 Faithful circuit cover; 2.2 3-edge-coloring and faithful cover; Applications of Lemma 2.2.1; 2.3 Construction of contra pairs; Isaacs-Fleischner-Jackson product; 2.4 Open problems; 2.5 Exercises; Admissible eulerian weights; Faithful cover; Contra pairs. | |
| 505 | 8 | |a 3: Circuit chain and Petersen minor3.1 Weight decomposition and removable circuit; 3.2 Cubic minimal contra pair; 3.3 Minimal contra pair; 3.4 Structure of circuit chain; 3.5 Open problems; 3.6 Exercises; Structure of circuit chain; Girth for faithful cover; Miscellanies; 4: Small oddness; 4.1 k-even subgraph double covers; 4.2 Small oddness; 4.3 Open problems; 4.4 Exercises; 5: Spanning minor, Kotzig frames; 5.1 Spanning Kotzig subgraphs; Generalizations of Kotzig graphs; Various spanning minors; 5.2 Kotzig frames; Proof of Theorem 5.2.6; 5.3 Construction of Kotzig graphs. | |
| 505 | 8 | |a 5.4 Three-Hamilton circuit double coversStrong Kotzig graphs; Uniquely 3-edge-colorable graphs; Hamilton weighted graphs; 5.5 Open problems; From frames to CDC; Existence of Kotzig frames; 5.6 Exercises; Constructions; Examples, counterexamples; Spanning minors; 6: Strong circuit double cover; 6.1 Circuit extension and strong CDC; 6.2 Thomason's lollipop method; Almost Hamilton circuit; 6.3 Stable circuits; 6.4 Extension-inheritable properties; 6.5 Extendable circuits; 6.6 Semi-extension of circuits; Further generalizations; 6.7 Circumferences; 6.8 Open problems; 6.9 Exercises. | |
| 505 | 8 | |a 7: Spanning trees, supereulerian graphs7.1 Jaeger Theorem: 2-even subgraph covers; Supereulerian graphs, even subgraph covers; Spanning trees, supereulerian graphs; 4-edge-connected graphs; 7.2 Jaeger Theorem: 3-even subgraph covers; Smallest counterexample to the theorem; The first proof of Theorem 7.2.1; The second proof of Theorem 7.2.1; 7.3 Even subgraph 2k-covers; 4-covers; 6-covers; Berge-Fulkerson conjecture; 7.4 Catlin's collapsible graphs; Examples of collapsible graphs; Maximal collapsible subgraph and graph reduction; Contractible configurations; 7.5 Exercises. | |
| 505 | 8 | |a 3-even subgraph coversBerge-Fulkerson conjecture; Collapsible graphs; 8: Flows and circuit covers; 8.1 Jaeger Theorems: 4-flow and 8-flow; 8.2 4-flows; Even subgraph covers; Parity subgraph decompositions; Evenly spanning even subgraphs; Faithful cover; 8.3 Seymour Theorem: 6-flow; Even subgraph 6-covers; 8.4 Contractible configurations for 4-flow; 8.5 Bipartizing matching, flow covering; 8.6 Exercises; 4-flows; Faithful covers; Seymour's operation; Miscellanies; 9: Girth, embedding, small cover; 9.1 Girth; 9.2 Small genus embedding; 9.3 Small circuit double covers; 9.4 Exercises. | |
| 520 | |a Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Graph theory. | |
| 650 | 0 | |a Graph theory |v Problems, exercises, etc. | |
| 650 | 7 | |a MATHEMATICS |x Graphic Methods. |2 bisacsh | |
| 650 | 7 | |a Teoría de grafos |2 embne | |
| 650 | 7 | |a Graph theory |2 fast | |
| 655 | 7 | |a Problems and exercises |2 fast | |
| 758 | |i has work: |a Circuit double cover of graphs (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFF9Wr9h6xCG6gc87JhQ4m |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Zhang, Cun-Quan. |t Circuit Double Cover of Graphs. |d Cambridge : Cambridge University Press, ©2012 |z 9780521282352 |
| 830 | 0 | |a London Mathematical Society Lecture Note Series, 399. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=880644 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 11.1 Restricted circuit decompositions -- 11.2 Open problems -- 11.3 Exercises -- 12: Reductions of weights, coverages -- 12.1 Weight reduction for contra pairs -- Application of Theorem 12.1.1 -- Outline of the proof of Theorem 12.1.1 -- Notation and lemmas -- Admissible dipath -- A technical lemma for adjustment of faithful cover -- V. Summary -- Proof of Theorem 12.1.1 -- Part one -- Part two -- 12.2 Coverage reduction with fixed parity -- 12.3 Exercises -- 13: Orientable cover -- 13.1 Orientable double cover -- Orientable 3-even subgraph double covers -- Orientable 4-even subgraph double covers -- 13.2 Circular double covers and modulo orientations -- Circular double covers -- Modulo orientations -- 13.3 Open problems -- 13.4 Exercises -- 14: Shortest cycle covers -- 14.1 Shortest cover and double cover -- 14.2 Minimum eulerian weight -- Faithful coverable graphs -- Smallest parity subgraphs -- Chinese postman problem -- 14.3 3-even subgraph covers -- 14.3.1 Basis of cycle space -- 14.3.2 3-even subgraph covers -- 14.3.3 (>= 4)-even subgraph covers -- 14.3.4 Upper bounds of SCC3 -- 14.3.5 Relations with other major conjectures -- Berge-Fulkerson conjecture -- Tutte's 5-flow conjecture -- Tutte's 3-flow conjecture -- Summary -- 14.3.6 Fano plane and Fano flows -- (A) Elements of the Fano plane -- (B) Fano flow 3-even subgraph cover -- (C) Fano points edge set partition -- (D) Fano lines vertex set partition -- (E) Fano line even subgraph -- (F) Fano basis 3-even subgraph cover -- 14.3.7 Incomplete Fano flows, Fμ-flows -- Line-incomplete, Fμ-flows -- Point-incomplete -- F4-flows, F5-flows and 2-factors -- 14.3.8 Some proofs -- Berge-Fulkerson conjecture and SCC3 -- Fano flows and SCC3 -- 14.4 Open problems -- 14.5 Exercises -- 15: Beyond integer (1, 2)-weight -- A uniform definition in linear/integer programming. | |
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