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.

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.

The CDC conjecture (and its numerous variants) is considered one of the major open problems in graph theory. This up-to-date overview of the subject contains all of the techniques, methods and results developed since the 1940s to help mathematicians and computer scientists still working towards a solution.

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