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.
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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.
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Circuit Double Cover of Graphs

Circuit Double Cover of Graphs

by Cun-Quan Zhang
Circuit Double Cover of Graphs

Circuit Double Cover of Graphs

by Cun-Quan Zhang

Paperback(New Edition)

$72.00 
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Overview

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.

Product Details

ISBN-13: 9780521282352
Publisher: Cambridge University Press
Publication date: 04/26/2012
Series: London Mathematical Society Lecture Note Series , #399
Edition description: New Edition
Pages: 375
Product dimensions: 5.98(w) x 8.90(h) x 0.79(d)

About the Author

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

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.
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