# A Semi-strong Perfect Digraph Theorem

## TL;DR

This paper extends Reed's theorem from undirected graphs to directed graphs, establishing conditions under which perfect digraphs are characterized by $P_4$-isomorphism.

## Contribution

It introduces a semi-strong perfect digraph theorem, providing a new characterization of perfect digraphs based on $P_4$-isomorphism.

## Key findings

- Analogous result for perfect digraphs derived
- Characterization of perfect digraphs via $P_4$-isomorphism established
- Extension of Reed's theorem from graphs to digraphs

## Abstract

Reed showed that, if two graphs are $P_4$-isomorphic, then either both are perfect or none of them is. In this note we will derive an analogous result for perfect digraphs.