Patrick Morris

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20242026

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3 papers · 1 filter

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…