Patrick Morris

collaborators

7 papers

math.CO2026

Slow graph bootstrap percolation I: Cycles

David Fabian, Patrick Morris, Tibor SzabÃ³

Given a fixed graph $H$ and an $n$ -vertex graph $G$ , the $H$ \emph{-bootstrap percolation process} on $G$ is defined to be the sequence of graphs $G_{i}$ , $i \geq 0$ which starts with…

math.CO2026

Two-round Ramsey games on random graphs

Yahav Alon, Patrick Morris, Wojciech Samotij

Motivated by the investigation of sharpness of thresholds for Ramsey properties in random graphs, Friedgut, Kohayakawa, RÃ¶dl, RuciÅski and Tetali introduced two variants of a sin…

math.CO2026

Schur properties of randomly perturbed sets

Shagnik Das, Charlotte Knierim, Patrick Morris

A set $A$ of integers is said to be \emph{Schur} if any two-colouring of $A$ results in monochromatic $x, y$ and $z$ with $x + y = z$ . We study the following problem: how many random in…

math.CO2026

A Ramsey-TurÃ¡n theory for tilings in graphs

Jie Han, Patrick Morris, Guanghui Wang +1

For a $k$ -vertex graph $F$ and an $n$ -vertex graph $G$ , an $F$ -tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$ . For $r \in N$ , the $r$ -independence nu…

math.CO2026

Vertex Ramsey properties of randomly perturbed graphs

Shagnik Das, Patrick Morris, Andrew Treglown

Given graphs $F, H$ and $G$ , we say that $G$ is $(F, H)_{v}$ -Ramsey if every red/blue vertex colouring of $G$ containsa red copy of $F$ or a blue copy of $H$ . Results of Åuczak, RuciÅ…

math.CO2026

Finding any given 2-factor in sparse pseudorandom graphs efficiently

Jie Han, Yoshiharu Kohayakawa, Patrick Morris +1

Given an $n$ -vertex pseudorandom graph $G$ and an $n$ -vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$ , i.e.\ an embedding $Ï\colon V(H)\to V…