Large Sets of Oriented $P_3$-Decompositions of Directed Complete Bipartite Graphs

Abstract

Let $H$ and $G$ be two graphs (or digraphs), where $G$ is a subgraph of $H$. A $G$-decomposition of $H$, denoted by $(H,G)$-GD, is a partition of all the edges (or arcs) of $H$ into subgraphs ($G$-blocks), each of which is isomorphic to $G$. A large set of $(H,G)$-GD, denoted by $(H,G)$-LGD, is a partition of all subgraphs isomorphic to $G$ of $H$ into $(H,G)$-GDs. In this paper, we obtain the existence spectra of $(AD{K}_{m,n},P_3^i)$-LGD, where $P_3^i$ ($i=1,2,3$) are the three types of oriented $P_3$.