Multidecompositions of Complete Bipartite Graphs into Cycles and Stars

Abstract

Let \(C_k\) denote a cycle of length \(k\) and let \(S_k\) denote a star with \(k\) edges. For graphs \(F\), \(G\), and \(H\), a \((G, H)\)-multidecomposition of \(F\) is a partition of the edge set of \(F\) into copies of \(G\) and copies of \(H\) with at least one copy of \(G\) and at least one copy of \(H\). In this paper, necessary and sufficient conditions for the existence of the \((C_k, S_k)\)-multidecomposition of a complete bipartite graph are given.