On the inducibility of oriented graphs on four vertices

TL;DR

This paper investigates the maximum asymptotic density of induced copies of oriented graphs on four vertices, providing exact values for many cases and close bounds for others, revealing complex extremal structures.

Contribution

It offers the first comprehensive determination of inducibility for all oriented graphs on four vertices, including exact values and bounds, and analyzes complex extremal configurations.

Findings

Exact inducibility values for over half of the graphs.

Close bounds for remaining graphs.

Complex structures of extremal configurations.

Abstract

We consider the problem of determining the inducibility (maximum possible asymptotic density of induced copies) of oriented graphs on four vertices. We provide exact values for more than half of the graphs, and very close lower and upper bounds for all the remaining ones. It occurs that, for some graphs, the structure of extremal constructions maximizing density of its induced copies is very sophisticated and complex.