Some gregarious kite decompositions of complete equipartite graphs
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چکیده
منابع مشابه
Some gregarious kite decompositions of complete equipartite graphs
A k-cycle decomposition of a multipartite graph G is said to be gregarious if each k-cycle in the decomposition intersects k distinct partite sets of G. In this paper we prove necessary and sufficient conditions for the existence of such a decomposition in the case where G is the complete equipartite graph, having n parts of size m, and either n ≡ 0, 1 (mod k), or k is odd and m ≡ 0 (mod k). As...
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The complete multipartite graph Kn(m) with n parts of size m is shown to have a decomposition into n-cycles in such a way that each cycle meets each part of Kn(m); that is, each cycle is said to be gregarious. Furthermore, gregarious decompositions are given which are also resolvable. © 2007 Elsevier B.V. All rights reserved.
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متن کاملA Note on Decomposition of Complete Equipartite Graphs into Gregarious 6-cycles
In [8], it is shown that the complete multipartite graph Kn(2t) having n partite sets of size 2t, where n ≥ 6 and t ≥ 1, has a decomposition into gregarious 6-cycles if n ≡ 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 n ≡ 0 or 3 (mod 6), another method using difference set is presented. Furthermore, wh...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.10.017