Uniformly Resolvable Cycle Decompositions with Four Different Factors

Abstract

In this paper, we consider uniformly resolvable decompositions of complete graph $$K_v$$ (or $$K_v$$ minus a 1-factor I for even v) into cycles. We will focus on the existence of factorizations of $$K_v$$ or $$K_v-I$$ containing up to four non-isomorphic factors. We obtain all possible solutions for uniform factors involving 4, m, 2m and 4m-cycles with a few possible exceptions when m is odd.