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Circuit Double Cover of Graphs

$67.99 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: May 2012
  • availability: Available
  • format: Paperback
  • isbn: 9780521282352

$ 67.99 (C)

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About the Authors
  • 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.

    • 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
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    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

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    Product details

    • Date Published: May 2012
    • format: Paperback
    • isbn: 9780521282352
    • length: 375 pages
    • dimensions: 226 x 152 x 20 mm
    • weight: 0.56kg
    • contains: 120 b/w illus. 200 exercises
    • availability: Available
  • Table of Contents

    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
    Author index
    Subject index.

  • Author

    Cun-Quan Zhang, West Virginia University
    Cun-Quan Zhang is Eberly Distinguished Professor of Mathematics at West Virginia University.

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