# Impartial digraphs

## TL;DR

This paper proves a conjecture characterizing directed graphs with constant density in all tournaments, showing they are disjoint unions of recursively constructed trees, advancing understanding of graph structures in combinatorics.

## Contribution

It provides a complete proof of a conjecture linking graph structure to density properties in tournaments, specifically identifying the form of graphs with uniform density.

## Key findings

- Directed graphs with constant density are disjoint unions of recursively constructed trees.
- The paper confirms the conjecture of Fox, Huang, and Lee.
- It advances the classification of graph structures in tournament theory.

## Abstract

We prove a conjecture of Fox, Huang, and Lee that characterizes directed graphs that have constant density in all tournaments: they are disjoint unions of trees that are each constructed in a certain recursive way.