Minimal defining sets of 1-factorizations of complete graphs - Cavenagh, Nicholas J.; Donovan, Diane; Khodkar, Abdollah (Utilitas Mathematica, 2008)
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 GKn (as defined in [1]) of Kn for each even n ≥ 4. Our construction exploits the well-known equivalence between 1-factorizations and unipotent, symmetric Latin squares.