Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2024

($\overrightarrow{P_6}$, triangle)-Free Digraphs Have Bounded Dichromatic Number

Résumé

The dichromatic number of an oriented graph is the minimum size of a partition of its vertices into acyclic induced subdigraphs. We prove that oriented graphs with no induced directed path on six vertices and no triangle have bounded dichromatic number. This is one (small) step towards the general conjecture asserting that for every oriented tree $T$ and every integer $k$, any oriented graph that does not contain an induced copy of $T$ nor a clique of size $k$ has dichromatic number at most some function of $k$ and $T$ .

Dates et versions

hal-04970384 , version 1 (27-02-2025)

Identifiants

Citer

Pierre Aboulker, Guillaume Aubian, Pierre Charbit, Stéphan Thomassé. ($\overrightarrow{P_6}$, triangle)-Free Digraphs Have Bounded Dichromatic Number. The Electronic Journal of Combinatorics, 2024, 31 (4), ⟨10.37236/11838⟩. ⟨hal-04970384⟩
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