dc.contributor.author Billington, Elizabeth J. dc.contributor.author Cavenagh, Nicholas J. dc.contributor.author Khodkar, Abdollah dc.date.accessioned 2013-02-17T20:53:10Z dc.date.available 2013-02-17T20:53:10Z dc.date.copyright 2012-08 dc.date.issued 2012 dc.identifier.citation Billington, E. J., Cavenagh, N. J., & Khodkar, A. (2012). Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems. Discrete Mathematics, 312(16), 2438-2445. en_NZ dc.identifier.issn 0012-365X dc.identifier.uri https://hdl.handle.net/10289/7208 dc.description.abstract Let (X,C) denote a twofold k-cycle system with an even number of cycles. If these k-cycles can be paired together so that: (i) each pair contains a common edge; (ii) removal of the repeated common edge from each pair leaves a (2k-2)-cycle; (iii) all the repeated edges, once removed, can be rearranged exactly into a collection of further (2k-2)-cycles; then this is a metamorphosis of a twofold k-cycle system into a twofold (2k-2)-cycle system. The existence of such metamorphoses has been dealt with for the case of 3-cycles (Gionfriddo and Lindner, 2003) [3] and 4-cycles (Yazc, 2005) [7]. If a twofold k-cycle system (X,C) of order n exists, which has not just one but has k different metamorphoses, from k different pairings of its cycles, into twofold (2k-2)-cycle systems, such that the collection of all removed double edges from all k metamorphoses precisely covers 2 Kn, we call this a complete set of twofold paired k-cycle metamorphoses into twofold (2k-2)-cycle systems. In this paper, we show that there exists a twofold 4-cycle system (X,C) of order n with a complete set of metamorphoses into twofold 6-cycle systems if and only if n≡0,1,9,16 (mod 24), n≠9. en_NZ dc.language.iso en dc.publisher Elsevier en_NZ dc.relation.ispartof Discrete Mathematics dc.subject Cycle decomposition en_NZ dc.subject Metamorphosis en_NZ dc.subject Twofold cycle system en_NZ dc.title Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems en_NZ dc.type Journal Article en_NZ dc.identifier.doi 10.1016/j.disc.2012.04.029 en_NZ dc.relation.isPartOf Discrete Mathematics en_NZ pubs.begin-page 2438 en_NZ pubs.elements-id 38214 pubs.end-page 2445 en_NZ pubs.issue 16 en_NZ pubs.volume 312 en_NZ uow.identifier.article-no 16 en_NZ
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