The Spectrum of $4$-Cycles in $2$-Factorizations of $K_{n,n}$

Abstract

A $2$-factor of a graph $G$ is a $2$-regular spanning subgraph of $G$ and a $2$-factorization of a graph $G$ is a $2$-factor decomposition of $G$. A complete solution to the problem of determining the spectrum of $4$-cycles in $2$-factorizations of the complete bipartite graph is presented.