Work

Acyclic Dichromatic Number of Tournaments: these are the Champions

Year: 2026

Type: preprint

Abstract: The acyclic dichromatic number of an oriented graph is the minimum size of a vertex-partition such that the digraphs induced by any single part are acyclic, and the oriented bipartite graphs between any two parts are acyclic too. We characterize the subtournaments that must appear in every tournament with sufficiently large acyclic dichromatic number, thereby confirming a conjecture of Bang-Jensen, Picasarri-Arrieta, and Yeo and prove that acyclic dichromatic number satisfies a local to global property.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.14694

Authors: Aboulker, Pierre, Charbit, Pierre, Coulomb, Samuel, Nurse, Kathryn, Picasarri-Arrieta, Lucas

Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, Département d'Informatique, Université Paris Cité, Institut de Recherche en Informatique Fondamentale, National Institute of Informatics

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Graph Algorithms and Optimization: Theory and Scalable Algorithms, G4379065183

OpenAlex ID: W7169602711

Cites: 1

Cited by: 1

Related to: 10