2022/07/19 by Soukaina Zayat, Zayat, Soukaina
Computer Science · Mathematics · #05C05 #05C20 #90C35 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2207.09146
openalex publication_date 2022/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An equivalent directed version of the celebrated unresolved conjecture of Erdos and Hajnal proposed by Alon et al. states 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)). A tournament H has the strong EH-property if there exists c > 0 such that for every H-free tournament T with |T| > 1, there exist disjoint vertex subsets A and B, each of cardinality at least c|T| and every vertex of A is adjacent to every vertex of B. Berger et al. proved that the unique five-vertex tournament denoted by C5, where every vertex has two inneighbors and two outneighbors has the strong EH-property. It is known that every tournament with the strong EH-property also has the EH-property. In this paper we construct an infinite class of tournaments - the so-called spiral galaxies and we prove that every spiral galaxy has the strong EH-property.