Author

Samuel Coulomb

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Preprint Sep 2026

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...

Pierre Charbit, Samuel Coulomb · 0 citations

Preprint Sep 2026

Clique Number of Tournaments II

The directed clique number $\vec{\omega}(T)$ of a tournament $T$ is the minimum, over all orderings of the vertices of $T$, of the clique number of the graph whose edges are the arcs that point backward with respect to the ordering. In this paper, we prove that, for every integer $k \geq 3$, deciding whether $\vec{\ome...

Guillaume Aubian, Samuel Coulomb · 0 citations