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

• Cho, Jung-R. ;
• Gould, Ronald J.
• Published : 2008.11.01
• 99 6

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

References

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Cited by

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2. ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t)INTO GREGARIOUS m-CYCLES vol.29, pp.3, 2013, https://doi.org/10.7858/eamj.2013.024
3. A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES vol.44, pp.4, 2007, https://doi.org/10.4134/BKMS.2007.44.4.709
4. CIRCULANT DECOMPOSITIONS OF CERTAIN MULTIPARTITE GRAPHS INTO GREGARIOUS CYCLES OF A GIVEN LENGTH vol.30, pp.3, 2014, https://doi.org/10.7858/eamj.2014.021