\(k\)-cycle free one-factorizations of complete graphs
Summary: It is proved that for every \(n\geq 3\) and every even \(k\geq 4\), where \(k\neq 2n\), there exists one-factorization of the complete graph \(K_{2n}\) such that any two one-factors do not induce a graph with a cycle of length \(k\) as a component. Moreover, some infinite classes of one-factorizations, in which lengths of cycles induced by any two one-factors satisfy a given lower bound, are constructed.
scientific article; zbMATH DE number 5541068