6 citations · 10 across the 5 of their papers we have counts for
10 papers
The strong component structure of the barely subcritical directed configuration model
Matthew Coulson
We study the behaviour of the largest components of the directed configuration model in the barely subcritical regime. We show that with high probability all strongly connected com…
Largest component of subcritical random graphs with given degree sequence
Matthew Coulson, Guillem Perarnau
We study the size of the largest component of two models of random graphs with prescribed degree sequence, the configuration model (CM) and the uniform model (UM), in the (barely)…
The typical approximate structure of sets with bounded sumset
Marcelo Campos, Matthew Coulson, Oriol Serra +1
Let and be randomly chosen subsets of the first integers of cardinalities , such that their sumset has size . We show that asympt…
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…
The critical window in random digraphs
Matthew Coulson
We consider the component structure of the random digraph inside the critical window .We show that the largest component has size o…
A Rainbow Dirac's Theorem
Matthew Coulson, Guillem Perarnau
A famous theorem of Dirac states that any graph on vertices with minimum degree at least has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this res…
Rainbow factors in hypergraphs
Matthew Coulson, Peter Keevash, Guillem Perarnau +1
For any -graph , we consider the problem of finding a rainbow -factor in an -graph with large minimum -degree and an edge-colouring that is suitably bounded.…
Rainbow matchings in Dirac bipartite graphs
Matthew Coulson, Guillem Perarnau
We show the existence of rainbow perfect matchings in -bounded edge colourings of Dirac bipartite graphs, for a sufficiently small . As an application of our results, we o…
Compound Poisson approximation of subgraph counts in stochastic block models with multiple edges
Matthew Coulson, Robert E. Gaunt, Gesine Reinert
We use the Stein-Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic…
Poisson approximation of subgraph counts in stochastic block models and a graphon model
Matthew Coulson, Robert E. Gaunt, Gesine Reinert
Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of…