The Hamilton-Waterloo Problem for Triangle-Factors and Heptagon-Factors

Abstract

Given 2-factors and of order , let and be nonnegative integers with , the Hamilton-Waterloo problem asks for a 2-factorization of if is odd, or of if is even, in which of its 2-factors are isomorphic to and the other 2-factors are isomorphic to . In this paper, we solve the problem for the case of triangle-factors and heptagon-factors for odd with 3 possible exceptions when .