Uniformly resolvable decompositions of $K_v$ into one $1$-factor and $n$-stars when $n>1$ is odd

Abstract

We consider uniformly resolvable decompositions of $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We give a complete solution for the case in which one resolution class is $K_2$ and the rest are $K_{1,n}$ where $n>1$ is odd.