Circuit Double Cover of Graphs.:
Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
|
| Schriftenreihe: | London Mathematical Society Lecture Note Series, 399.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture. |
| Beschreibung: | 1 online resource (381 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139376440 1139376446 0521282357 9780521282352 9781107263598 110726359X 9781139379304 1139379305 9781139375016 1139375016 9780511863158 0511863152 |
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| 245 | 1 | 0 | |a Circuit Double Cover of Graphs. |
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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. | ||
| 650 | 0 | |a Graph theory. |0 http://id.loc.gov/authorities/subjects/sh85056471 | |
| 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. | |
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| 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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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn794327665 |
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| _version_ | 1816881795474391040 |
| adam_text | |
| any_adam_object | |
| author | Zhang, Cun-Quan |
| author_facet | Zhang, Cun-Quan |
| author_role | |
| author_sort | Zhang, Cun-Quan |
| author_variant | c q z cqz |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166 |
| callnumber-search | QA166 |
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| callnumber-subject | QA - Mathematics |
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| contents | 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. 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. 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. 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. 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. |
| ctrlnum | (OCoLC)794327665 |
| dewey-full | 511.5 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 511/.5 |
| dewey-search | 511.5 511/.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Graph theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85056471</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Graph theory</subfield><subfield code="v">Problems, exercises, etc.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Graphic Methods.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Teoría de grafos</subfield><subfield code="2">embne</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Graph theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="a">Problems and exercises</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Circuit double cover of graphs (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFF9Wr9h6xCG6gc87JhQ4m</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Zhang, Cun-Quan.</subfield><subfield code="t">Circuit Double Cover of Graphs.</subfield><subfield code="d">Cambridge : Cambridge University Press, ©2012</subfield><subfield code="z">9780521282352</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society Lecture Note Series, 399.</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=443712</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="8" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="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.</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH23028222</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">22580054</subfield><subfield code="c">45.00 GBP</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL880644</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10565026</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">443712</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">363329</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7665551</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7651029</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">8871522</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7636089</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| genre | Problems and exercises fast |
| genre_facet | Problems and exercises |
| id | ZDB-4-EBA-ocn794327665 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:24Z |
| institution | BVB |
| isbn | 9781139376440 1139376446 0521282357 9780521282352 9781107263598 110726359X 9781139379304 1139379305 9781139375016 1139375016 9780511863158 0511863152 |
| language | English |
| oclc_num | 794327665 |
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| publisher | Cambridge University Press, |
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| series | London Mathematical Society Lecture Note Series, 399. |
| series2 | London Mathematical Society Lecture Note Series, 399 ; |
| spelling | Zhang, Cun-Quan. Circuit Double Cover of Graphs. Cambridge : Cambridge University Press, 2012. 1 online resource (381 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file London Mathematical Society Lecture Note Series, 399 ; v. 399 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. 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. 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. 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. 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. Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture. Print version record. Includes bibliographical references and index. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Graph theory Problems, exercises, etc. MATHEMATICS Graphic Methods. bisacsh Teoría de grafos embne Graph theory fast Problems and exercises fast has work: Circuit double cover of graphs (Text) https://id.oclc.org/worldcat/entity/E39PCFF9Wr9h6xCG6gc87JhQ4m https://id.oclc.org/worldcat/ontology/hasWork Print version: Zhang, Cun-Quan. Circuit Double Cover of Graphs. Cambridge : Cambridge University Press, ©2012 9780521282352 London Mathematical Society Lecture Note Series, 399. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=443712 Volltext 505-00/(S 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. |
| spellingShingle | Zhang, Cun-Quan Circuit Double Cover of Graphs. London Mathematical Society Lecture Note Series, 399. 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. 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. 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. 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. 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. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Graph theory Problems, exercises, etc. MATHEMATICS Graphic Methods. bisacsh Teoría de grafos embne Graph theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85056471 |
| 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. |
| title_fullStr | Circuit Double Cover of Graphs. |
| title_full_unstemmed | Circuit Double Cover of Graphs. |
| title_short | Circuit Double Cover of Graphs. |
| title_sort | circuit double cover of graphs |
| topic | Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Graph theory Problems, exercises, etc. MATHEMATICS Graphic Methods. bisacsh Teoría de grafos embne Graph theory fast |
| topic_facet | Graph theory. Graph theory Problems, exercises, etc. MATHEMATICS Graphic Methods. Teoría de grafos Graph theory Problems and exercises |
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| work_keys_str_mv | AT zhangcunquan circuitdoublecoverofgraphs |