The Hamilton—Waterloo problem: The case of triangle‐factors and one Hamilton cycle

Abstract

Abstract The Hamilton—Waterloo problem is to determine the existence of a 2‐factorization of K 2 n +1 in which r of the 2‐factors are isomorphic to a given 2‐factor R and s of the 2‐factors are isomorphic to a given 2‐factor S , with r + s = n . In this article we consider the case when R is a triangle‐factor, S is a Hamilton cycle and s = 1. We solve the problem completely except for 14 possible exceptions. This solves a major open case from the 2004 article of Horak et al. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 160–176, 2009