Cycles in Graphs

B.R. Alspach, C.D. Godsil

• Publisher: North Holland
• Year: 1985
• Print ISBN: 9780444878038
• eBook ISBN: 9780080872261
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.

Table of contents

• Front Cover
• Cycle in Graphs
• Copyright Page
• Table of Contents
• Foreword
• Chapter 1. A Survey of the Cycle Double Cover Conjecture
• Chapter 2. A Girth Requirement for the Double Cycle Cover Conjecture
• Chapter 3. Hamilton Cycles in Metacirculant Graphs with Prime Cardinality Blocks
• Chapter 4. Hamilton Paths in Cartesian Products of Directed Cycles
• Chapter 5. Every Connected Cayley Graph of a Group with Prime Order Commutator Group Has a Hamilton Cycle
• Chapter 6. Multiple-Ply Hamiltonian Graphs and Digraphs
• Chapter 7. On Hamilton Cycles in Cayley Graphs in Groups with Cyclic Commutator Subgroup
• Chapter 8. Hamilton Circuits in Cartesian Products with a Metacyclic Factor
• Chapter 9. Vertex Transitive Graphs and Digraphs of Order pk
• Chapter 10. Some Hamiltonian Cayley Graphs
• Chapter 11. On Hamilton Cycles in 3-Connected Cubic Maps
• Chapter 12. Non-Hamiltonian 3-Polytopes Whose Faces Are All Pentagons
• Chapter 13. Hamilton Circuits in Regular Tournaments
• Chapter 14. Circuits and Hamilton Circuits in Domination Orientable Tournaments
• Chapter 15. First Occurrence of Hamilton Cycles in Random Graphs
• Chapter 16. The Pancyclicity of Halin Graphs and their Exterior Contractions
• Chapter 17. Long Paths between Specified Vertices of a Block
• Chapter 18. Longest Cycles in 2-Connected Graphs of Independence Number α
• Chapter 19. A Note on Maximal Cycles in 2-Connected Graphs
• Chapter 20. A Note on Isomorphic Generalized Prisms
• Chapter 21. Uniformly n-Cyclic Graphs
• Chapter 22. Cycles in 3-Connected Cubic Planar Graphs
• Chapter 23. A Lemma on Cycle Decompositions
• Chapter 24. A Note on Hamilton Cycles
• Chapter 25. A Counterexample to a Conjecture about Oriented Graphs
• Chapter 26. An Improvement of Jackson's Result on Hamilton Cycles in 2-Connected Regular Graphs
• Chapter 27. Finding Cycles of a Given Length
• Chapter 28. Clique Coverings of Complements of Paths and Cycles
• Chapter 29. Equicardinal Disjoint Cycles in Sparse Graphs
• Chapter 30. Path and Cycle Decompositions of Complete Multigraphs
• Chapter 31. Minimum Number of Circuits Covering the Vertices of a Strong Digraph
• Chapter 32. On Decomposing Graphs into Isomorphic Uniform 2-Factors
• Chapter 33. Two Complementary Circuits in Two-Connected Tournaments
• Chapter 34. The Clique Partition Number of the Complement of a Cycle
• Chapter 35. The Computational Complexity of Decomposing Block Designs
• Chapter 36. Kotzig's Conjecture on Generalized Friendship Graphs - A Survey
• Chapter 37. A Short Proof of Rubin's Block Theorem
• Chapter 38. Cycle Basis Interpolation Theorems
• Chapter 39. A Basis for the Cycle Space of a 3-Connected Graph
• Chapter 40. Types of Cycles in Hypergraphs
• Chapter 41. Parity of Cycles Containing Specified Edges
• Chapter 42. An Optimal Algorithm for Directing Triple Systems Using Eulerian Circuits
• Chapter 43. The Reconstruction Conjecture for Balanced Signed Graphs
• Chapter 44. Periodic Points of Small Periods of Continuous Mappings of Trees
• Chapter 45. Periodic Points of Continuous Mappings of Trees
• Chapter 46. Unsolved Problems