David A. Pike

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7 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.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

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 $T \subseteq S$ ,…