CLASS OF STARTER INDUCED 1-FACTORIZATIONS.

Abstract

A technique of R. C. Mullin and E. Nemeth for constructing strong starters in certain Abelian groups of prime power order is considered. These strong starters induce 1-factorizations of complete graphs. The method is applied to construct what is apparently the first example of a 1-factorization of the complete graph on 28 points, K//2//8, such that the union of every two distinct 1-factors is a Hamiltonian circuit. This problem generalized to K//2//n, has arisen in several contexts and the results obtained strengthens the conjecture of various authors that such 1-factorizations exist on all K//2//n.