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http://dx.doi.org/10.4134/JKMS.2008.45.6.1623

DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES  

Cho, Jung-R. (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
Gould, Ronald J. (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE EMORY UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.6, 2008 , pp. 1623-1634 More about this Journal
Abstract
The complete multipartite graph $K_{n(2t)}$ having n partite sets of size 2t, with $n\;{\geq}\;6$ and $t\;{\geq}\;1$, is shown to have a decomposition into gregarious 6-cycles, that is, the cycles which have at most one vertex from any particular partite set. Complete sets of differences of numbers in ${\mathbb{Z}}_n$ are used to produce starter cycles and obtain other cycles by rotating the cycles around the n-gon of the partite sets.
Keywords
multipartite graph; graph decomposition; gregarious cycle; difference set;
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