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Circuit Double Cover of Graphs: London Mathematical Society Lecture Note Series, cartea 399

Autor Cun-Quan Zhang
en Limba Engleză Paperback – 25 apr 2012
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.
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Specificații

ISBN-13: 9780521282352
ISBN-10: 0521282357
Pagini: 375
Ilustrații: 120 b/w illus. 200 exercises
Dimensiuni: 152 x 226 x 20 mm
Greutate: 0.54 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria London Mathematical Society Lecture Note Series

Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

"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

Notă biografică


Descriere

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