Complex uniformly resolvable decompositions of $K_v$

Abstract

In this paper we consider the complex uniformly resolvable decompositions of the complete graph $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph from a given set $\mathcal{H}$. We completely determine the spectrum for the cases $\mathcal{H}=\{K_2,P_3,K_3\}$, $\mathcal{H}=\{P_4,C_4\}$, and $\mathcal{H}=\{K_2,P_4,C_4\}$.

11 pages