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arXiv · 2010.12329

Erdös-Hajnal Conjecture for New Infinite Families of Tournaments

Soukaina Zayat·Salman Ghazal
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Abstract

Erdös-Hajnal conjecture states that for every undirected graph $H$ there exists $ ε(H) > 0 $ such that every undirected graph on $ n $ vertices that does not contain $H$ as an induced subgraph contains a clique or a stable set of size at least $ n^{ε(H)} $. This conjecture has a directed equivalent version stating that for every tournament $H$ there exists $ ε(H) > 0 $ such that every $H-$free $n-$vertex tournament $T$ contains a transitive subtournament of order at least $ n^{ε(H)} $. This conjecture is known to hold for a few infinite families of tournaments. In this paper we construct two new infinite families of tournaments - the family of so-called galaxies with spiders and the family of so-called asterisms, and we prove the correctness of the conjecture for these two families.

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BibTeXRIS

Soukaina Zayat, Salman Ghazal. 2022-08-08. Erdös-Hajnal Conjecture for New Infinite Families of Tournaments. https://arxiv.org/abs/2010.12329

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