{Ck, Pk, Sk} -Decompositions of Balanced Complete Bipartite Multigraphs

Abstract

Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of Hi, where . Let Ck, Pk and Sk denote a cycle, a path and a star with k edges, respectively. For an integer , we prove that a balanced complete bipartite multigraph  has a -decomposition if and only if k is even, and .