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 : Thursday 21 November 2024

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