A. Burgess

activity

20152026

most citedOn the Hamilton-Waterloo Problem with odd orders

5 citations · 7 across the 12 of their papers we have counts for

collaborators

Showing math.COShow all

13 papers · 1 filter

math.CO2026

Burning Steiner triple systems

Andrea C. Burgess, Peter H. Danziger, Caleb W. Jones +2

Graph burning is a round-based process which can be viewed as a discrete one-player game that models the spread of influence throughout a network. Extending this process to hypergr…

math.CO2026

Locally Semi-Equitable Colourings of BIBDs

Andrea C. Burgess, William Kellough, David A. Pike

We study $ℓ$ -colourings of $(v, k, λ)$ -BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the $ℓ - 1$ other colours appears exac…

math.CO2026

Uniquely 2-colourable 4-cycle decompositions

Andrea C. Burgess, David A. Pike, Shahriyar Pourakbar-Saffar

A cycle system of order $n$ is a decomposition of the edges of the complete graph $K_{n}$ into cycles of a fixed length. A cycle system is said to be $k$ -colourable if we can assign…

math.CO2026

A complete solution to the directed Oberwolfach problem of order $2 (mod 4)$ with cycles of even lengths

A. C. Burgess, P. H. Danziger, A. Lacaze-Masmonteil

The Oberwolfach problem asks for a $2$ -factorization of the complete graph in which each $2$ -factor is isomorphic to a specific factor $F$ . Recently, this problem has been extended…

math.CO2025

Colourings of Uniform Group Divisible Designs and Maximum Packings

Andrea C Burgess, Peter Danziger, Diane Donovan +4

A weak $c$ -colouring of a design is an assignment of colours to its points from a set of $c$ available colours, such that there are no monochromatic blocks. A colouring of a design…

math.CO2024

Packing Designs with large block size

Andrea C. Burgess, Peter Danziger, Daniel Horsley +1

Given positive integers $v$ , $k$ , $t$ and $λ$ with $v \geq k \geq t$ , a packing design PD $_{λ} (v, k, t)$ is a pair $(V, B)$ , where $V$ is a $v$ -set and $B$ is a coll…

math.CO2024

Proportion-Based Hypergraph Burning

Andrea C. Burgess, John A. Hawkin, Alexander J. M. Howse +2

Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently…

math.CO2024

Existential Closure in Uniform Hypergraphs

Andrea C. Burgess, Robert D. Luther, David A. Pike

For a positive integer $n$ , a graph with at least $n$ vertices is $n$ -existentially closed or simply $n$ -e.c. if for any set of vertices $S$ of size $n$ and any set $T \subseteq S$ ,…

math.CO2024

Weak colourings of Kirkman triple systems

Andrea C. Burgess, Nicholas J. Cavenagh, Peter Danziger +1

A $δ$ -colouring of the point set of a block design is said to be {\em weak} if no block is monochromatic. The {\em chromatic number} $χ (S)$ of a block design $S$ is the smallest in…

math.CO2024★ 2 cited

Extending Graph Burning to Hypergraphs

Andrea C. Burgess, Caleb W. Jones, David A. Pike

Graph burning is a round-based game or process that discretely models the spread of influence throughout a network. We introduce a generalization of graph burning which applies to…

math.CO2023

On equitably 2-colourable odd cycle decompositions

Andrea Burgess, Francesca Merola

An $ℓ$ -cycle decomposition of $K_{v}$ is said to be \emph{equitably $2$ -colourable} if there is a $2$ -vertex-colouring of $K_{v}$ such that each colour is represented (approximately…

math.CO2015★ 5 cited

On the Hamilton-Waterloo Problem with odd orders

A. Burgess, P. Danziger, T. Traetta

Given non-negative integers $v, m, n, α, β$ , the Hamilton-Waterloo problem asks for a factorization of the complete graph $K_{v}$ into $α$ $C_{m}$ -factors and $β$ $C_{n}$ -factors. Clearl…

math.CO2015

On generalized Howell designs with block size three

R. Julian R. Abel, Robert F. Bailey, Andrea C. Burgess +2

In this paper, we examine a class of doubly resolvable combinatorial objects. Let $t, k, λ, s$ and $v$ be nonnegative integers, and let $X$ be a set of $v$ symbols. A generalized H…

Burning Steiner triple systems

Locally Semi-Equitable Colourings of BIBDs

Uniquely 2-colourable 4-cycle decompositions

A complete solution to the directed Oberwolfach problem of order 2(mod4) with cycles of even lengths

Colourings of Uniform Group Divisible Designs and Maximum Packings

Packing Designs with large block size

Proportion-Based Hypergraph Burning

Existential Closure in Uniform Hypergraphs

Weak colourings of Kirkman triple systems

Extending Graph Burning to Hypergraphs

On equitably 2-colourable odd cycle decompositions

On the Hamilton-Waterloo Problem with odd orders

On generalized Howell designs with block size three

A complete solution to the directed Oberwolfach problem of order $2 (mod 4)$ with cycles of even lengths