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- W4290802703 abstract "Erd{o}s-Hajnal conjecture states that for every undirected graph $H$ there exists $ epsilon(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^{epsilon(H)} $. This conjecture has a directed equivalent version stating that for every tournament $H$ there exists $ epsilon(H) > 0 $ such that every $H-$free $n-$vertex tournament $T$ contains a transitive subtournament of order at least $ n^{epsilon(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." @default.
- W4290802703 created "2022-08-12" @default.
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- W4290802703 date "2020-10-22" @default.
- W4290802703 modified "2023-09-23" @default.
- W4290802703 title "Erd{o}s-Hajnal Conjecture for New Infinite Families of Tournaments" @default.
- W4290802703 doi "https://doi.org/10.48550/arxiv.2010.12329" @default.
- W4290802703 hasPublicationYear "2020" @default.
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