Multi-decomposition of complete bipartite graphs and complete graphs into banners and stars of size five

Abstract

A decomposition of a graph G is a set of edge disjoint subgraphs H1, H2, ..., Hr of G such that every edge of G belongs to exactly one Hi. If all the subgraphs in the decomposition of G are isomorphic to a graph H, then we say that G is H-decomposable. The graph G has an (H1, H2)-multi-decomposition if α copies of H1 and β copies of H2 decompose G, where α and β are non-negative integers. In this paper, we have obtained the multi-decomposition of complete bipartite graphs and complete graphs into banners and stars of size 5.