Résumé : In this talk, we consider the probability space of random digraphs defined as follow. We generate a random undirected graph by taking the classical Erdős–Rényi model $\mathbb G(n,p)$. Thereafter, each edge is given a direction, where each of the two directions has probability $\frac{1}{2}$ and all choices are made independently. The result is a simple digraph on $n$ vertices. We will study the the probability that a random digraph is acyclic when $p=O(1/n)$, i.e. it does not contain a directed cycle when the number of edges is linear in the number of vertices. This is a joint work with Dimbinaina Ralaivaosaona and Stephan Wagner.

Dernière modification : Tuesday 11 February 2025

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr