S. Bessy

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20242026

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math.CO2026

A relaxation of the Bermond-Thomassen conjecture

Stéphane Bessy, Matthijs Muis, Jean-Sébastien Sereni +2

The well-known Bermond-Thomassen conjecture states that every digraph of minimum out-degree at least $2 k - 1$ contains $k$ vertex-disjoint directed cycles. Despite being posed in 198…

math.CO2025

Plane Strong Connectivity Augmentation

StÃ©phane Bessy, Daniel GonÃ§alves, Amadeus Reinald +1

We investigate the problem of strong connectivity augmentation within plane oriented graphs. We show that deciding whether a plane oriented graph $D$ can be augmented with (any num…

math.CO2025

Dichromatic number of chordal graphs

The dichromatic number of a digraph is the minimum integer $k$ such that it admits a $k$ -dicolouring, i.e. a partition of its vertices into $k$ acyclic subdigraphs. We say that a d…

math.CO2024

Oriented trees in $O (k k)$ -chromatic digraphs, a subquadratic bound for Burr's conjecture

In 1980, Burr conjectured that every directed graph with chromatic number $2 k - 2$ contains any oriented tree of order $k$ as a subdigraph. Burr showed that chromatic number $(k-1)^2…

A relaxation of the Bermond-Thomassen conjecture

Plane Strong Connectivity Augmentation

Dichromatic number of chordal graphs

Oriented trees in O(kk​)-chromatic digraphs, a subquadratic bound for Burr's conjecture

Oriented trees in $O (k k)$ -chromatic digraphs, a subquadratic bound for Burr's conjecture