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.
Title The extended metamorphosis of a complete bipartite design into a cycle system
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1016/j.disc.2003.11.025
Volume 284
Issue 1-3
Start page 63
End page 70
Total pages 8
Editor P. L. Hammer
Place of publication Netherlands
Publisher Elsevier BV
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract 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.
Keyword Mathematics
Fold Block-designs
Triple-systems
Size-4
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 13:04:51 EST