dc.contributor.author Billington, Elizabeth J. dc.contributor.author Cavenagh, Nicholas J. dc.date.accessioned 2012-01-31T02:01:23Z dc.date.available 2012-01-31T02:01:23Z dc.date.issued 2011 dc.identifier.citation Billington, E.J., Cavenagh, N.J. (2011). Decomposing complete tripartite graphs into 5-cycles when the partite sets have similar size. Aequationes Mathematicae, 82(3), 277-289. en_NZ dc.identifier.uri https://hdl.handle.net/10289/5992 dc.description.abstract The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph into 5-cycles was first posed at a conference in 1994 (Mahmoodian and Mirzakhani in Combinatorics Advances, 1995). Since then, many cases of the problem have been solved by various authors; however the case when the partite sets have odd and distinct sizes remains open. In this note, we introduce a new approach to the problem by embedding previously known decompositions into larger ones. Via this approach, we show that when the partite sets have asymptotically similar sizes, the conjectured necessary conditions for a decomposition are also sufficient. en_NZ dc.language.iso en dc.publisher Springer en_NZ dc.relation.uri http://www.springerlink.com/content/g27vxk3871171584/ en_NZ dc.subject graph decomposition en_NZ dc.subject cycle decomposition en_NZ dc.subject complete tripartite graph en_NZ dc.title Decomposing complete tripartite graphs into 5-cycles when the partite sets have similar size en_NZ dc.type Journal Article en_NZ dc.identifier.doi 10.1007/s00010-011-0098-6 en_NZ dc.relation.isPartOf Aequationes Mathematicae en_NZ pubs.begin-page 277 en_NZ pubs.elements-id 36812 pubs.end-page 289 en_NZ pubs.issue 3 en_NZ pubs.volume 82 en_NZ
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