# The extended metamorphosis of a complete bipartite design into a cycle system

Billington, E. J. (2004) The extended metamorphosis of a complete bipartite design into a cycle system. Discrete Mathematics, 284 1-3: 63-70. doi:10.1016/j.disc.2003.11.025

Author Billington, E. J. The extended metamorphosis of a complete bipartite design into a cycle system Discrete Mathematics   Check publisher's open access policy 0012-365X 2004-01-01 Article (original research) 10.1016/j.disc.2003.11.025 Not yet assessed 284 1-3 63 70 8 P. L. Hammer Netherlands Elsevier BV eng C1230101 Mathematical Logic, Set Theory, Lattices And Combinatorics780101 Mathematical sciences A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved. MathematicsFold Block-designsTriple-systemsSize-4 C1 UQ

 Document type: Journal Article Article (original research) Excellence in Research Australia (ERA) - Collection School of Mathematics and Physics 2005 Higher Education Research Data Collection

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