The Hamilton-Waterloo Problem with C-4 and C-m factors

Abstract

The Hamilton Waterloo problem with uniform cycle sizes asks for a 2-factorization of the complete graph K-v (for odd v) or K-v minus a 1-factor (for even v) where r of the factors consist of n-cycles and s of the factors consist of m-cycles with r + s = [v-1/2]. In this paper, the Hamilton Waterloo Problem with 4-cycle and m-cycle factors for odd m >= 3 is studied and all possible solutions with a few possible exceptions are determined. (C) 2015 Elsevier B.V. All rights reserved.