Factorizations of complete graphs into cycles and 1-factors

Abstract

In this paper, we consider factorizations of complete graph $K_v$ into cycles and $1$--factors. We will focus on the existence of factorizations of $K_v$ containing two nonisomorphic factors. We obtain all possible solutions for uniform factors involving $m$--cycles and $1$--factors with a few possible exceptions when $m$ is odd.