Patrick Morris

activity

20242026

collaborators

5 papers

math.CO2026

Universal probability bounds for partial Latin squares

Jack Allsop, Patrick Morris

This paper studies the probability of substructures occurring in random Latin squares. Our main result states that if $I^\pm, I^^{2} > 0$ are such that $2 I^\pm + I^^{2} < 1$ , then there are positive co…

math.CO2026

Graph bootstrap percolation -- a discovery of slowness

David Fabian, Patrick Morris, Tibor SzabÃ³

Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of $K_{n}$ . Given an initial set $G \subseteq K_{n}$ of infected edges, the transmiss…

math.CO2026

A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs

Amarja Kathapurkar, Patrick Morris, Guillem Perarnau

A meta-conjecture of Coulson, Keevash, Perarnau and Yepremyan states that above the extremal threshold for a given spanning structure in a (hyper-)graph, one can find a rainbow ver…

math.CO2025

Slow graph bootstrap percolation III: Chain constructions

David Fabian, Patrick Morris, Tibor SzabÃ³

For graphs $H$ , we study the extremal function $M_{H} (n)$ which is the maximum running time (until stabilisation) of an $H$ -bootstrap percolation process on $n$ vertices. Building on…

math.CO2024

Slow graph bootstrap percolation II: Accelerating properties

David Fabian, Patrick Morris, Tibor SzabÃ³

For a graph $H$ and an $n$ -vertex graph $G$ , the $H$ -bootstrap process on $G$ is the process which starts with $G$ and, at every time step, adds any missing edges on the vertices o…