{Ck, Pk, Sk}-Decompositions of Balanced Complete Bipartite Graphs
نویسندگان
چکیده
Let L = {H1, H2, . . . ,Hr} be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer αi copies of Hi, where i ∈ {1, 2, . . . , r}. Let Ck, Pk and Sk denote a cycle, a path and a star with k edges, respectively. In this paper, we prove that a balanced complete bipartite graph with 2n vertices has a {Ck, Pk, Sk}-decomposition if and only if k is even, 4 ≤ k ≤ n and n2 ≡ 0 (mod k). Mathematics Subject Classification: 05C51
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