Minimal Defining Sets of 1-Factorizations of Complete Graphs

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. In this paper we construct minimal defining sets of size (n - 4)(n +2)/4 in the 1-factorizations GK(n) (as defined in [1]) of K-n for each even n >= 4. Our construction exploits the well-known equivalence between 1-factorizations and unipotent, symmetric Latin squares