Cycles in Graphs

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B.R. Alspach, C.D. Godsil
Elsevier, Aug 1, 1985 - Mathematics - 466 pages
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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.
 

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Contents

Chapter 1 A Survey of the Cycle Double Cover Conjecture
1
Chapter 2 A Girth Requirement for the Double Cycle Cover Conjecture
13
Chapter 3 Hamilton Cycles in Metacirculant Graphs with Prime Cardinality Blocks
27
Chapter 4 Hamilton Paths in Cartesian Products of Directed Cycles
35
Chapter 5 Every Connected Cayley Graph of a Group with Prime Order Commutator Group Has a Hamilton Cycle
75
Chapter 6 MultiplePly Hamiltonian Graphs and Digraphs
81
Chapter 7 On Hamilton Cycles in Cayley Graphs in Groups with Cyclic Commutator Subgroup
89
Chapter 8 Hamilton Circuits in Cartesian Products with a Metacyclic Factor
103
Chapter 25 A Counterexample to a Conjecture about Oriented Graphs
235
Chapter 26 An Improvement of Jacksons Result on Hamilton Cycles in 2Connected Regular Graphs
237
Chapter 27 Finding Cycles of a Given Length
249
Chapter 28 Clique Coverings of Complements of Paths and Cycles
257
Chapter 29 Equicardinal Disjoint Cycles in Sparse Graphs
269
Chapter 30 Path and Cycle Decompositions of Complete Multigraphs
275
Chapter 31 Minimum Number of Circuits Covering the Vertices of a Strong Digraph
287
Chapter 32 On Decomposing Graphs into Isomorphic Uniform 2Factors
297

Chapter 9 Vertex Transitive Graphs and Digraphs of Order pk
115
Chapter 10 Some Hamiltonian Cayley Graphs
129
Chapter 11 On Hamilton Cycles in 3Connected Cubic Maps
141
Chapter 12 NonHamiltonian 3Polytopes Whose Faces Are All Pentagons
151
Chapter 13 Hamilton Circuits in Regular Tournaments
159
Chapter 14 Circuits and Hamilton Circuits in Domination Orientable Tournaments
163
Chapter 15 First Occurrence of Hamilton Cycles in Random Graphs
173
Chapter 16 The Pancyclicity of Halin Graphs and their Exterior Contractions
179
Chapter 17 Long Paths between Specified Vertices of a Block
195
Chapter 18 Longest Cycles in 2Connected Graphs of Independence Number α
201
Chapter 19 A Note on Maximal Cycles in 2Connected Graphs
205
Chapter 20 A Note on Isomorphic Generalized Prisms
209
Chapter 21 Uniformly nCyclic Graphs
215
Chapter 22 Cycles in 3Connected Cubic Planar Graphs
219
Chapter 23 A Lemma on Cycle Decompositions
227
Chapter 24 A Note on Hamilton Cycles
233
Chapter 33 Two Complementary Circuits in TwoConnected Tournaments
321
Chapter 34 The Clique Partition Number of the Complement of a Cycle
335
Chapter 35 The Computational Complexity of Decomposing Block Designs
345
Chapter 36 Kotzigs Conjecture on Generalized Friendship Graphs A Survey
351
Chapter 37 A Short Proof of Rubins Block Theorem
367
Chapter 38 Cycle Basis Interpolation Theorems
369
Chapter 39 A Basis for the Cycle Space of a 3Connected Graph
381
Chapter 40 Types of Cycles in Hypergraphs
399
Chapter 41 Parity of Cycles Containing Specified Edges
419
Chapter 42 An Optimal Algorithm for Directing Triple Systems Using Eulerian Circuits
433
Chapter 43 The Reconstruction Conjecture for Balanced Signed Graphs
439
Chapter 44 Periodic Points of Small Periods of Continuous Mappings of Trees
443
Chapter 45 Periodic Points of Continuous Mappings of Trees
447
Chapter 46 Unsolved Problems
461
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