# Cycles in Graphs

**Edited By**

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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### Book information

- Published: January 1985
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-87803-8

### Table of Contents

A Survey of the Cycle Double Cover Conjecture (F. Jaeger). A Girth Requirement for the Double Cycle Cover Conjecture (L. Goddyn). Hamilton Cycles in Metacirculant Graphs with Prime Cardinality Blocks (B. Alspach, E. Durnberger and T.D. Parsons). Hamilton Paths in Cartesian Products of Directed Cycles. (S.J. Curran and D. Witte). Every Connected Cayley Graph of a Group with Prime Order Commutator Group has a Hamilton Cycle (E. Durnberger). Multiple-Ply Hamiltonian Graphs and Digraphs (K. Keating). On Hamilton Cycles in Cayley Graphs in Groups with Cyclic Commutator Subgroup (K. Keating and D. Witte). Hamilton Circuits in Cartesian Products with a Metacyclic Factor (G. Letzter). Vertex Transitive Graphs and Digraphs of Order pk (D. Marušič). Some Hamiltonian Cayley Graphs (D.L. Powers). On Hamilton Cycles in 3-Connected Cubic Maps (L. Bruce Richmond, R.W. Robinson and N.C. Wormwald). Non-Hamiltonian 3-Polytopes Whose Faces Are All Pentagons (P.J. Owens). Hamilton Circuits in Regular Tournaments (C. Thomassen). Circuits and Hamilton Circuits in Domination Orientable Tournaments (C.-Q. Zhang). First Occurrence of Hamilton Cycles in Random Graphs (M. Ajtai, J. Komlós and E. Szenerédi). The Pancyclicity of Halin Graphs and their Exterior Contractions (M. Skowrońska). Long Paths between Specified Vertices of a Block (J.A. Bondy and B. Jackson). Longest Cycles in 2-Connected Graphs of Independence Number &agr; (L. Fournier). A Note on Maximal Cycles in 2-Connected Graphs (R. Häggkvist and B. Jackson). A Note on Isomorphic Generalized Prisms (S.P. Mohanty and D. Rao). Uniformly n-Cyclic Graphs (D. Wagner). Cycles in 3-Connected Cubic Planar Graphs (D.A. Holton). A Lemma on Cycle Decompositions (R. Häggkvist). A Note on Hamilton Cycles (R. Häggkvist). A Counterexample to a Conjecture about Oriented Graphs (L. Goddyn). An Improvement of Jackson's Result on Hamilton Cycles in 2-Connected Regular Graphs (Z. Yongjin, L. Zhenong and Y. Zhengguang). Finding Cycles of a Given Length (D. Richards and A.L. Liestman). Clique Coverings of Complements of Paths and Cycles (D. de Caen, D.A. Gregory and N.J. Pullman). Equicardinal Disjoint Cycles in Sparse Graphs (R. Häggkvist). Path and Cycle Decompositions of Complete Multigraphs (K. Heinrich and G.M. Nonay). Minimum Number of Circuits Covering the Vertices of a Strong Digraph (M.C. Heydemann). On Decomposing Graphs into Isomorphic Uniform 2-Factors (J.D. Horton et al.). Two Complementary Circuits in Two-Connected Tournaments (K.B. Reid). The Clique Partition Number of the Complement of a Cycle (W.D. Wallis). The Computational Complexity of Decomposing Block Designs (C.J. Colbourn and M.J. Colbourn). Kotzig's Conjecture on Generalized Friendship Graphs - A Survey (J.A. Bondy). A Short Proof of Rubin's Block Theorem (R.C. Entringer). Cycle Basis Interpolation Theorems (F. Harary, E. Kolasińska and M.M. Syslo). A Basis for the Cycle Space of a 3-Connected Graph (S.C. Locke). Types of Cycles in Hypergraphs (R. Duke). Parity of Cycles Containing Specified Edges (W.D. McCuaig and M. Rosenfeld). An Optimal Algorithm for Directing Triple Systems Using Eulerian Circuits (J.J. Harms and C.J. Colbourn). The Reconstruction Conjecture for Balanced Signed Graphs (F. Harary). Periodic Points of Small Periods of Continuous Mappings of Trees (W. Imrich). Periodic Points of Continuous Mappings of Trees (W. Imrich and R. Kalinowski). Unsolved Problems.