Unavoidable Subtournaments in Tournaments with Large Chromatic Number
Combinatorics
2018-04-16 v1
Abstract
For a set H of tournaments, we say H is heroic if every tournament, not containing any member of H as a subtournament, has bounded chromatic number. Berger et al. explicitly characterized all heroic sets containing one tournament. Motivated by this result, we study heroic sets containing two tournaments. We give a necessary condition for a set containing two tournaments to be heroic. We also construct infinitely many minimal heroic sets of size two.
Cite
@article{arxiv.1804.04787,
title = {Unavoidable Subtournaments in Tournaments with Large Chromatic Number},
author = {Ilhee Kim and Ringi Kim},
journal= {arXiv preprint arXiv:1804.04787},
year = {2018}
}