Franklin

Circuit double cover of graphs [electronic resource] / Cun-Quan Zhang.

Author/Creator:
Zhang, Cun-Quan, 1952-
Publication:
Cambridge : Cambridge University Press, 2012.
Series:
London Mathematical Society lecture note series ; 399.
London Mathematical Society lecture note series ; 399
Format/Description:
Book
1 online resource (381 p.)
Subjects:
Graph theory -- Problems, exercises, etc.
Combinatorial analysis.
Form/Genre:
Electronic books.
Language:
English
Summary:
Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture.
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
Embedded graphs
Notes:
Description based upon print version of record.
Include bibligraphical references (p.[337]-349) and index.
ISBN:
1-107-22396-2
0-511-86315-2
1-280-64724-8
9786613633293
1-139-37787-6
1-139-37501-6
1-139-37644-6
1-139-37930-5
1-139-37102-9
OCLC:
794327665
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