Maximum uniformly resolvable decompositions of $K_v$ and $K_v-I$ into 3-stars and 3-cycles

Abstract

Let $K_v$ denote the complete graph of order $v$ and $K_v-I$ denote $K_v$ minus a 1-factor. In this article we investigate uniformly resolvable decompositions of $K_v$ and $K_v-I$ into $r$ classes containing only copies of $3$-stars and $s$ classes containing only copies of $3$-cycles. We completely determine the spectrum in the case where the number of resolution classes of 3-stars is maximum.