Asymptotic Enumeration of $I_3$-free Digraphs

TL;DR

This paper proves that nearly all digraphs avoiding an independent set of size 3 are composed of two disjoint tournaments, linking their structure to homogeneous simple structures.

Contribution

It establishes the asymptotic structure of $I_3$-free digraphs and connects this to the theory of homogeneous simple structures.

Findings

Almost all $I_3$-free digraphs are two disjoint tournaments.

The structure of these digraphs is characterized asymptotically.

Connections are made with the theory of homogeneous simple structures.

Abstract

We prove that almost all digraphs not embedding an independent set of size 3 consist of two disjoint tournaments, and discuss connections with the theory of homogeneous simple structures.