Title

On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity

Document Type

Article

Publication Date

11-25-2019

Department

Department of Mathematical Sciences

Abstract

The Hamilton-Waterloo problem asks for a decomposition of the complete graph of order v into r copies of a 2-factor F1 and s copies of a 2-factor F2 such that r+s = v−1 2 . If F1 consists of m-cycles and F2 consists of n cycles, we say that a solution to (m, n)- HWP(v; r, s) exists. The goal is to find a decomposition for every possible pair (r, s). In this paper, we show that for odd x and y, there is a solution to (2kx, y)-HWP(vm; r, s) if gcd(x, y) ≥ 3, m ≥ 3, and both x and y divide v, except possibly when 1 ∈ {r, s}.

Publisher's Statement

© This work is licensed under https://creativecommons.org/licenses/by/4.0/. Publisher’s version of record: https://doi.org/10.26493/1855-3974.1610.03d

Publication Title

ARS MATHEMATICA CONTEMPORANEA

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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