On 1-factorizations of complete graphs

Abstract

A defining set of a 1 - factorization of a graph G is a set of partial 1-factors of G which may be completed to a unique 1-factorization of G. We construct defining sets of size n² - 3n + 4 in a 1-factorization of K_2n for each n > 3 and give a sharp upper bound for the minimum size of a defining set among all 1-factorizations of K_2n.