Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2008.11.01
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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.

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References

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  1. Some gregarious kite decompositions of complete equipartite graphs vol.313, pp.5, 2013, https://doi.org/10.1016/j.disc.2012.10.017
  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