A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES

Title & Authors
A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES
Cho, Jung-Rae;

Abstract
In [8], it is shown that the complete multipartite graph $\small{K_{n(2t)}}$ having n partite sets of size 2t, where $\small{n{\geq}6\;and\;t{\geq}1}$, has a decomposition into gregarious 6-cycles if $\small{n{\equiv}0,1,3}$ or 4 (mod 6). Here, a cycle is called gregarious if it has at most one vertex from any particular partite set. In this paper, when $\small{n{\equiv}0}$ or 3 (mod 6), another method using difference set is presented. Furthermore, when $\small{n{\equiv}0}$ (mod 6), the decomposition obtained in this paper is $\small{{\infty}-circular}$, in the sense that it is invariant under the mapping which keeps the partite set which is indexed by $\small{{\infty}}$ fixed and permutes the remaining partite sets cyclically.
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.
Some gregarious kite decompositions of complete equipartite graphs, Discrete Mathematics, 2013, 313, 5, 726
3.
ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t)INTO GREGARIOUS m-CYCLES, East Asian mathematical journal, 2013, 29, 3, 337
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