Constructing uniform 2-factorizations via row-sum matrices: Solutions to the Hamilton-Waterloo problem

被引：2

作者：

Burgess, A. C. ^{[1
]}

Danziger, P. ^{[2
]}

Pastine, A. ^{[3
,4
]}

Traetta, T. ^{[5
]}

机构：

[1] Univ New Brunswick, Dept Math & Stat, 100 Tucker Pk Rd, St John, NB E2L 4L5, Canada

[2] Toronto Metropolitan Univ, Dept Math, 350 Victoria St, Toronto, ON M5B 2K3, Canada

[3] CONICET UNSL, Inst Matemat Aplicada San Luis, Ejercito Andes 950, RA-5700 San Luis, Argentina

[4] Univ Nacl San Luis, Dept Matemat, Ejercito Andes 950, RA-5700 San Luis, Argentina

[5] Univ Brescia, DICATAM, Via Branze 43, I-25123 Brescia, Italy

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2024年 / 201卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

2-factorizations; Resolvable cycle decompositions; Cycle systems; Generalized Oberwolfach problem; Hamilton-Waterloo problem; Row-sum matrices; OBERWOLFACH PROBLEM; SIZES;

D O I：

10.1016/j.jcta.2023.105803

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group G. When G is cyclic, these types of matrices have been widely used to build uniform 2-factorizations of small Cayley graphs (or, Cayley subgraphs of blown-up cycles), which themselves factorize complete (equipartite) graphs. Here, we construct row-sum matrices over a class of non-abelian groups, the generalized dihedral groups, and we use them to construct uniform 2-factorizations that solve infinitely many open cases of the Hamilton-Waterloo problem, thus filling up large parts of the gaps in the spectrum of orders for which such factorizations are known to exist. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：26