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.

- Cover
- Title Page
- Copyright
- Dedication Page
- Contents
- Foreword (by Brian Alspach)
- Foreword (by Michael Tarsi)
- Preface
- Chapter 1: Circuit Double Cover
- Chapter 2: Faithful Circuit Cover
- Chapter 3: Circuit Chain and Petersen Minor
- Chapter 4: Small Oddness
- Chapter 5: Spanning Minor, Kotzig Frames
- Chapter 6: Strong Circuit Double Cover
- Chapter 7: Spanning Trees, Supereulerian Graphs
- Chapter 8: Flows and Circuit Covers
- Chapter 9: Girth, Embedding, Small Cover
- Chapter 10: Compatible Circuit Decompositions
- Chapter 11: Other Circuit Decompositions
- Chapter 12: Reductions of Weights, Coverages
- Chapter 13: Orientable Cover
- Chapter 14: Shortest Cycle Covers
- Chapter 15: Beyond Integer (1, 2)-Weight
- Chapter 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