5-cycle decompositions from paired 3- and 4-cycle decompositions

Billington, Elizabeth J. (2011) 5-cycle decompositions from paired 3- and 4-cycle decompositions. Australasian Journal of Combinatorics, 51 109-113.

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Author Billington, Elizabeth J.
Title 5-cycle decompositions from paired 3- and 4-cycle decompositions
Journal name Australasian Journal of Combinatorics   Check publisher's open access policy
ISSN 1034-4942
Publication date 2011-10
Sub-type Article (original research)
Volume 51
Start page 109
End page 113
Total pages 5
Place of publication The University of Queensland, Qld., Australia
Publisher Centre for Discrete Mathematics and Computing
Collection year 2012
Language eng
Abstract Let (V,T) be a 3-fold triple system and (V,C) a 4-fold 4-cycle system on the same set V. This choice of indices 3 and 4 ensures that each system contains the same number of cycles: {pipe}T{pipe} = {pipe}C{pipe}. We pair up the cycles, {t, c}, where t ∈ T and c ∈ C, in such a way that t and c share one edge. If t = (x, y, z) and c = (x, y, u, v), so t and c share the edge {x, y}, then we retain the 5-cycle (z, x, v, u, y) and remove the repeated edge {x, y}. Doing this for all the pairs {t, c}, we rearrange all the shared edges, common to t and c, into further 5-cycles, so that the result is a 7-fold 5-cycle system on V. The necessary conditions are that the order {pipe}V {pipe} is 1 or 5 (mod 10); these conditions are shown to be sufficient for such a "metamorphosis" from pairs of 3- and 4-cycles into 5-cycles.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
 
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Created: Wed, 25 Jan 2012, 11:53:28 EST by Kay Mackie on behalf of School of Mathematics & Physics