A Note on Decomposition of Complete Equipartite Graphs into Gregarious 6-cycles
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چکیده
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, when n ≡ 0 (mod 6), the decomposition obtained in this paper is ∞-circular, in the sense that it is invariant under the mapping which keeps the partite set which is indexed by ∞ fixed and permutes the remaining partite sets cyclically.
منابع مشابه
Some gregarious kite decompositions of complete equipartite graphs
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