Some results and problems on tournament structure - Nguyen, T; Scott, A; Seymour, P (Elsevier, 2025)
This paper is a survey of results and problems related to the following question: is it true that if G is a tournament with sufficiently large chromatic number, then G has two vertex-disjoint subtournaments A, B, both with large chromatic number, such that all edges between them are directed from A to B? We describe what we know about this question, and report some progress on several other related questions, on tournament colouring and domination.