A. Burgess

activity

20152022

most citedOn the directed Oberwolfach Problem with equal cycle lengths: the odd case

5 citations · 6 across the 4 of their papers we have counts for

collaborators

8 papers

math.CO2022

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

A. C. Burgess, P. Danziger, A. Pastine +1

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…

math.CO2022

Mutually orthogonal cycle systems

Andrea C. Burgess, Nicholas J. Cavenagh, David A. Pike

An $ℓ$ -cycle system $F$ of a graph $Γ$ is a set of $ℓ$ -cycles which partition the edge set of $Γ$ . Two such cycle systems $F$ and $F^{'}$ ar…

math.CO2019

Cyclic cycle systems of the complete multipartite graph

Andrea Burgess, Francesca Merola, Tommaso Traetta

In this paper, we study the existence problem for cyclic $ℓ$ -cycle decompositions of the graph $K_{m} [n]$ , the complete multipartite graph with $m$ parts of size $n$ , and give nec…

math.CO2019

The Firebreak Problem

Kathleen D. Barnetson, Andrea C. Burgess, Jessica Enright +3

Suppose we have a network that is represented by a graph $G$ . Potentially a fire (or other type of contagion) might erupt at some vertex of $G$ . We are able to respond to this outb…

math.CO2018

The Hamilton-Waterloo Problem with even cycle lengths

A. C. Burgess, P. Danziger, T. Traetta

The Hamilton-Waterloo Problem HWP $(v; m, n; α, β)$ asks for a 2-factorization of the complete graph $K_{v}$ or $K_{v} - I$ , the complete graph with the edges of a 1-factor removed, into $α$ …

math.CO2018

On the Hamilton-Waterloo Problem with cycle lengths of distinct parities

Andrea Burgess, Peter Danziger, Tommaso Traetta

Let $K_{v}^{*}$ denote the complete graph $K_{v}$ if $v$ is odd and $K_{v} - I$ , the complete graph with the edges of a 1-factor removed, if $v$ is even. Given non-negative integers $v, M, N…