A. Burgess

collaborators

7 papers

math.CO2026

Locally Semi-Equitable Colourings of BIBDs

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

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

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

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.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

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.CO2025

Packing Designs with large block size

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

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

Locally Semi-Equitable Colourings of BIBDs

Uniquely 2-colourable 4-cycle decompositions

Colourings of Uniform Group Divisible Designs and Maximum Packings

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

Extending Graph Burning to Hypergraphs

Packing Designs with large block size

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