Brian Hearn

collaborators

3 papers

math.CO2026

Reconstructing a graph from its Bell colouring graph

Brian Hearn

The Bell colouring graph $B (G)$ of a graph $G$ is the graph whose vertices are the partitions of the vertex set of $G$ into independent sets, with an edge between two par…

math.CO2026

Spanning tight components in 4-uniform hypergraphs

Francesco Di Braccio, Brian Hearn, Joanna Lada +2

We prove that every $n$ -vertex 4-uniform hypergraph with minimum codegree at least $⌊ n /4 ⌋$ has a spanning tight component. This is tight, and it settles the 4-uniform…

math.CO2025

Determining a graph from its reconfiguration graph

Given a graph $G$ and a natural number $k$ , the $k$ -recolouring graph $C_{k} (G)$ is the graph whose vertices are the $k$ -colourings of $G$ and whose edges link pairs of col…