Characterizing Large Clique Number in Tournaments
Combinatorics
2026-02-11 v1 Discrete Mathematics
Abstract
Aboulker, Aubian, Charbit, and Lopes (2023) defined the clique number of a tournament to be the minimum clique number of one of its backedge graphs. Here we show that if is a tournament of sufficiently large clique number, then contains a subtournament of large clique number from one of two simple families of tournaments. In particular, large clique number is always certified by a bounded-size set. This answers a question of Aboulker, Aubian, Charbit, and Lopes (2023), and gives new insight into a line of research initiated by Kim and Kim (2018) into unavoidable subtournaments in tournaments with large dichromatic number.
Keywords
Cite
@article{arxiv.2602.09863,
title = {Characterizing Large Clique Number in Tournaments},
author = {Logan Crew and Xinyue Fan and Hidde Koerts and Benjamin Moore and Sophie Spirkl},
journal= {arXiv preprint arXiv:2602.09863},
year = {2026}
}