## Cycles in GraphsThis 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

1 | |

13 | |

27 | |

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 |

### Common terms and phrases

2-connected graph 2-factors 3-circuit adjacent algorithm assume bipartite cartesian product Cayley graph clique Combinatorial component connected contradiction COROLLARY coset cubic graph cycle basis cycle in Cay cycle in G cycle of length cycle space cyclic decomposed defined degree denote digraph Discrete Math disjoint dominates double cover double cycle cover elements Elsevier Science Publishers endpoint endvertices eulerian exactly one edge exists Figure finite G contains graph G Graph Theory Hamilton circuit Hamilton cycle Hamilton path Hamiltonian cycles Hence hypergraph implies induced intersection Lemma length at least Let G m-cycles matroid multigraph notation NP-complete number of edges obtained p-group pair pancyclic partition path of length periodic point planar graph point of period problem proof of Theorem Proposition prove Publishers B.V. North-Holland result Science Publishers B.V. sequence signed graph subgraph subset Suppose tournament triangle triple system vertex transitive vertices of G