Український математичний конгрес  2009
Nader Jafari Rad (Shahrood University of Technology, Shahrood, Iran) A conjecture on complete graphs A defining set of 1factorizations of a graph G is a set of partial 1factors of G which may be completed to a unique 1factorization of G. We construct defining sets of size n^{2}3n+4 in a 1factorization of K_{2n} for each n ≤ 3 and give an (improved) upper bound for the minimum size of a defining set among all 1factorizations of K_{2n}.
