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 $T$ is a tournament of sufficiently large clique number, then $T$ 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.

翻译：Aboulker、Aubian、Charbit和Lopes（2023）将竞赛图的团数定义为其任一后边图团数的最小值。本文证明，若竞赛图$T$具有足够大的团数，则$T$必然包含来自两个简单竞赛图族之一的、具有大团数的子竞赛图。特别地，大团数总可由一个有界大小的集合所验证。这一结论回答了Aboulker、Aubian、Charbit和Lopes（2023）提出的问题，并为Kim和Kim（2018）所开创的、关于大二色数竞赛图中不可避免子竞赛图的研究方向提供了新的见解。