Decompositions of balanced complete bipartite graphs into suns and stars

Abstract

Let L = {H 1 , H 2 ,. .. , H r } be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer α i copies of H i , where i ∈ {1, 2,. .. , r}. Let S(C k/2) and S k denote a sun and a star with k edges, respectively. In this paper, we prove that a balanced complete bipartite graph with 2n vertices has a {S(C k/2), S k }-decomposition if and only if 8 ≤ k ≤ n, k ≡ 0 (mod 4) and n 2 ≡ 0 (mod k).