$G$-Designs Having a Prescribed Number of Blocks in Common

Abstract

Two $G$-designs $(X,{\mathcal{A}}_1)$ and $(X,{\mathcal{A}}_2)$ are said to intersect in $m$ blocks if $|{\mathcal{A}}_1\cap {\mathcal{A}}_2|=m$. In this paper, we complete the solution of the intersection problem for $G$-designs, where $G$ is a connected graph of size five which contains a cycle.