Matthew Coulson

activity

20172019

collaborators

5 papers

cs.DS2019

Statistical physics approaches to Unique Games

Matthew Coulson, Ewan Davies, Alexandra Kolla +2

We show how two techniques from statistical physics can be adapted to solve a variant of the notorious Unique Games problem, potentially opening new avenues towards the Unique Game…

math.CO2019

The critical window in random digraphs

Matthew Coulson

We consider the component structure of the random digraph $D (n, p)$ inside the critical window $p = n^{- 1} + λ n^{- 4/3}$ .We show that the largest component $C_{1}$ has size o…

math.CO2018

A Rainbow Dirac's Theorem

Matthew Coulson, Guillem Perarnau

A famous theorem of Dirac states that any graph on $n$ vertices with minimum degree at least $n /2$ has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this res…

math.CO2018

Rainbow factors in hypergraphs

Matthew Coulson, Peter Keevash, Guillem Perarnau +1

For any $r$ -graph $H$ , we consider the problem of finding a rainbow $H$ -factor in an $r$ -graph $G$ with large minimum $ℓ$ -degree and an edge-colouring that is suitably bounded.…

math.CO2017

Rainbow matchings in Dirac bipartite graphs

Matthew Coulson, Guillem Perarnau

We show the existence of rainbow perfect matchings in $μ n$ -bounded edge colourings of Dirac bipartite graphs, for a sufficiently small $μ > 0$ . As an application of our results, we o…