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.