Circuit Double Cover of Graphs

Contains all the techniques, methods and results developed so far in a bid to solve the famous CDC conjecture.

Cun-Quan Zhang (Author)

9780521282352, Cambridge University Press

Paperback, published 26 April 2012

375 pages, 120 b/w illus. 200 exercises
22.6 x 15.2 x 2 cm, 0.56 kg

"This book draws a comprehensive panoramic image of material from a large number of results spread through various papers.The most essential of these results are virtually rewritten, and the fabric of connections among them is revealed. The author establishes a uniform framework in which most of the work done so far, as well as potential directions for future work, is described and can be understood in a clear and systematic manner. The book is recommended to researchers and students interested in graph theory."
Martin Kochol, Mathematical Reviews

The famous Circuit Double Cover conjecture (and its numerous variants) is considered one of the major open problems in graph theory owing to its close relationship with topological graph theory, integer flow theory, graph coloring and the structure of snarks. It is easy to state: every 2-connected graph has a family of circuits covering every edge precisely twice. C.-Q. Zhang provides an up-to-date overview of the subject containing all of the techniques, methods and results developed to help solve the conjecture since the first publication of the subject in the 1940s. It is a useful survey for researchers already working on the problem and a fitting introduction for those just entering the field. The end-of-chapter exercises have been designed to challenge readers at every level and hints are provided in an appendix.

Foreword
Preface
1. Circuit double cover
2. Faithful circuit cover
3. Circuit chain and Petersen minor
4. Small oddness
5. Spanning minor, Kotzig frames
6. Strong circuit double cover
7. Spanning trees, supereulerian graphs
8. Flows and circuit covers
9. Girth, embedding, small cover
10. Compatible circuit decompositions
11. Other circuit decompositions
12. Reductions of weights, coverages
13. Orientable cover
14. Shortest cycle covers
15. Beyond integer (1, 2)-weight
16. Petersen chain and Hamilton weights
Appendix A. Preliminary
Appendix B. Snarks, Petersen graph
Appendix C. Integer flow theory
Appendix D. Hints for exercises
Glossary of terms and symbols
References
Author index
Subject index.

Subject Areas: Discrete mathematics [PBD], Coding theory & cryptology [GPJ], Information theory [GPF]