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

Title & Authors
DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES
Cho, Jung-R.; Gould, Ronald J.;

Abstract
The complete multipartite graph $\small{K_{n(2t)}}$ having n partite sets of size 2t, with $\small{n\;{\geq}\;6}$ and $\small{t\;{\geq}\;1}$, 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 $\small{{\mathbb{Z}}_n}$ 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;
Language
English
Cited by
1.
ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES,;

East Asian mathematical journal , 2013. vol.29. 3, pp.337-347
2.
CIRCULANT DECOMPOSITIONS OF CERTAIN MULTIPARTITE GRAPHS INTO GREGARIOUS CYCLES OF A GIVEN LENGTH,;

East Asian mathematical journal , 2014. vol.30. 3, pp.311-319
1.
CIRCULANT DECOMPOSITIONS OF CERTAIN MULTIPARTITE GRAPHS INTO GREGARIOUS CYCLES OF A GIVEN LENGTH, East Asian mathematical journal , 2014, 30, 3, 311
2.
A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES, Bulletin of the Korean Mathematical Society, 2007, 44, 4, 709
3.
ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES, East Asian mathematical journal , 2013, 29, 3, 337
4.
Some gregarious kite decompositions of complete equipartite graphs, Discrete Mathematics, 2013, 313, 5, 726
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