Robert Morris

collaborators

4 papers

math.CO2026

On the ErdÅs-Rogers function

Robert Morris, Julian Sahasrabudhe, Jacques VerstraÃ«te

We show that the ErdÅs-Rogers function $f_{s, s + 1} (n)$ satisfies $f_{s, s + 1} (n) = I^ (n lo g n)$ for every $s \geq 2$ . More precisely, we construct a $K_{s + 1}$ -free graph o…

math.CO2026

Upper bounds for multicolour Ramsey numbers

Paul Balister, BÃ©la BollobÃ¡s, Marcelo Campos +5

The $r$ -colour Ramsey number $R_{r} (k)$ is the minimum $n \in N$ such that every $r$ -colouring of the edges of the complete graph $K_{n}$ on $n$ vertices contains a monochroma…

math.CO2026

Some recent results in Ramsey theory

Robert Morris

The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various gro…

math.CO2025

Random cliques in random graphs revisited

Robert Morris, Oliver Riordan

We study the distribution of the set of copies of some given graph $H$ in the random graph $G (n, p)$ , focusing on the case when $H = K_{r}$ . Our main results capture the 'leading term…

On the ErdÅs-Rogers function

Upper bounds for multicolour Ramsey numbers

Some recent results in Ramsey theory

Random cliques in random graphs revisited

On the ErdÅs-Rogers function