Some results and problems on tournament structure
Combinatorics
2024-09-25 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2306.02364,
title = {Some results and problems on tournament structure},
author = {Tung Nguyen and Alex Scott and Paul Seymour},
journal= {arXiv preprint arXiv:2306.02364},
year = {2024}
}