Barnaby Roberts

activity

20152022

most citedOn the average size of independent sets in triangle-free graphs

41 citations · 103 across the 10 of their papers we have counts for

collaborators

12 papers

math.CO2022

The Ramsey numbers of squares of paths and cycles

Peter Allen, Domenico Mergoni Cecchelli, Barnaby Roberts +1

The square $G^{2}$ of a graph $G$ is the graph on $V (G)$ with a pair of vertices $uv$ an edge whenever $u$ and $v$ have distance $1$ or $2$ in $G$ . Given graphs $G$ and $H$ , the Rams…

math.CO2022★ 1 cited

A robust Corrádi--Hajnal Theorem

Peter Allen, Julia Böttcher, Jan Corsten +5

For a graph $G$ and $p \in [0, 1]$ , we denote by $G_{p}$ the random sparsification of $G$ obtained by keeping each edge of $G$ independently, with probability $p$ . We show that there ex…

math.CO2018★ 2 cited

The multicolour size-Ramsey number of powers of paths

Jie Han, Matthew Jenssen, Yoshiharu Kohayakawa +2

Given a positive integer $s$ , a graph $G$ is $s$ -Ramsey for a graph $H$ , denoted $G \to (H)_{s}$ , if every $s$ -colouring of the edges of $G$ contains a monochromatic copy of $…

math.CO2017

The size-Ramsey number of powers of paths

Dennis Clemens, Matthew Jenssen, Yoshiharu Kohayakawa +4

Given graphs $G$ and $H$ and a positive integer $q$ say that $G$ is $q$ -Ramsey for $H$ , denoted $G \to (H)_{q}$ , if every $q$ -colouring of the edges of $G$ contains a monochro…

math.CO2017★ 3 cited

Tight bounds on the coefficients of partition functions via stability

Ewan Davies, Matthew Jenssen, Will Perkins +1

Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. Fo…

math.CO2016★ 15 cited

Extremes of the internal energy of the Potts model on cubic graphs

Ewan Davies, Matthew Jenssen, Will Perkins +1

We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs…