Matthew Coulson

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20172019

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4 papers · 1 filter

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…