David A. Pike

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8 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 $(v, k, I^»)$ -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.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

Weak colourings of Kirkman triple systems

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

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