63 citations · 189 across the 26 of their papers we have counts for
4 papers · 1 filter
Random graphs from a weighted minor-closed class
Colin McDiarmid
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we us…
Independent sets in graphs with given minimum degree
Hiu-Fai Law, Colin McDiarmid
We consider numbers and sizes of independent sets in graphs with minimum degree at least , when the number of vertices is large. In particular we investigate which of these…
Connectivity for random graphs from a weighted bridge-addable class
Colin McDiarmid
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable structured class, such as the class of all planar graphs. Here we cons…
Largest sparse subgraphs of random graphs
Nikolaos Fountoulakis, Ross J. Kang, Colin McDiarmid
For the Erdős-Rényi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most…