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arXiv · 1804.04787

Unavoidable Subtournaments in Tournaments with Large Chromatic Number

Ilhee Kim·Ringi Kim
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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.

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Ilhee Kim, Ringi Kim. 2018-04-13. Unavoidable Subtournaments in Tournaments with Large Chromatic Number. https://arxiv.org/abs/1804.04787

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