Circuit Double Cover of Graphs

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.

Spis treści:
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.