Circuit Double Cover of Graphs
Circuit Double Cover of Graphs
$67.99
USDThe 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.
- Terminology is listed in an appendix for those new to the field
- Includes A Mini Encyclopedia of the Petersen Graph
- Provides hints for selected exercises
Reviews & endorsements
"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
Product details
May 2012Paperback
9780521282352
375 pages
226 × 152 × 20 mm
0.56kg
120 b/w illus. 200 exercises
Available
Table of Contents
- 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.
