Pierre Charbit

Digraphs of Large Girth and Dichromatic Number in Tournaments with Large Dichromatic Number

In the 1960s, Erd\H{o}s and Hajnal conjectured that every graph with sufficiently large chromatic number contains a subgraph of large girth (size of a smallest cycle) and large chromatic number. In this paper, we prove that every tournament with sufficiently large dichromatic number contains a subdigraph of large digir...