Graphs and Matroids Seminar - Matthew Coulson

Title: Strong components of the directed configuration model

Abstract:

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 components in this regime are either cycles or isolated vertices and give an asymptotic distribution of the size of the kth largest cycle. This gives a configuration model analogue of a result of Luczak and Seierstad for the binomial random digraph.