On Large Sets of $K_{1,p}$-Decomposition of Complete Bipartite Graphs

Abstract

Let $H$ and $G$ be two simple graphs, where $G$ is a subgraph of $H$. A $G$-decomposition of $\lambda H$, denoted by $(\lambda H,G)$-GD, is a partition of all the edges of $\lambda H$ into subgraphs (G-blocks), each of which is isomorphic to $G$. A large set of $(\lambda H,G)$-GD, denoted by $(\lambda H,G)$-LGD, is a partition of all subgraphs isomorphic to $G$ of $H$ into $(\lambda H,G)$-GDs (called small sets). In this paper, we investigate the existence of $(\lambda K_{mn},K_{1,p})$-LGD and obtain some existence results, where $p\ge 3$ is a prime.