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The Ramsey number of fano plane versus tight path

Balogh, József, Clemen, Felix Cristian, Skokan, Jozef and Wgner, Adam Zsolt (2019) The Ramsey number of fano plane versus tight path. Electronic Journal of Combinatorics. ISSN 1077-8926 (In Press)

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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
Divisions: Mathematics
Date Deposited: 17 Oct 2019 12:15
Last Modified: 22 Jan 2020 00:26

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