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The Ramsey number of Fano plane versus tight path

Balogh, József, Clemen, Felix Cristian, Skokan, Jozef ORCID: 0000-0003-3996-7676 and Wgner, Adam Zsolt (2020) The Ramsey number of Fano plane versus tight path. Electronic Journal of Combinatorics, 27 (1). ISSN 1077-8926

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Identification Number: 10.37236/8374

Abstract

The hypergraph Ramsey number of two 3-uniform hypergraphs G and H, de- noted by R(G,H), is the least integer N such that every red-blue edge-coloring of the complete 3-uniform hypergraph on N vertices contains a red copy of G or a blue copy of H. The Fano plane F is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that R(H, F) ≥ 2(v(H) − 1) + 1. Hypergraphs H for which the equality holds are called F-good. Conlon asked to determine all H that are F-good. In this short paper we make progress on this problem and prove that the tight path of length n is F-good.

Item Type: Article
Official URL: https://www.combinatorics.org/ojs/index.php/eljc
Additional Information: © 2020 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 17 Oct 2019 12:15
Last Modified: 20 Oct 2021 02:44
URI: http://eprints.lse.ac.uk/id/eprint/102138

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