The Ramsey number of diamond-matchings and loose cycles in hypergraphs
type: Item
instance of: scholarly article
title: The Ramsey number of diamond-matchings and loose cycles in hypergraphs
zbMATH Open document ID: 1165.05334
author: András Gyárfás
author: Gábor N. Sárközy
author: Endre Szemerédi
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: v15i1r126.html
review text: Summary: The 2-color Ramsey number \(R({\mathcal{C}}_n^3,{\mathcal{C}}_n^3)\) of a 3-uniform loose cycle \({\mathcal{C}}_n\) is asymptotic to \(5n/4\) as has been recently proved by Haxell, Łuczak, Peng, Rödl, Ruciński, Simonovits and Skokan. Here we extend their result to the \(r\)-uniform case by showing that the corresponding Ramsey number is asymptotic to \(\frac{(2r-1)n}{2r-2}\). Partly as a tool, partly as a subject of its own, we also prove that for \(r\geq 2, R(kD_r,kD_r)=k(2r-1)-1\) and \(R(kD_r,kD_r,kD_r)=2kr-2\) where \(kD_r\) is the hypergraph having \(k\) disjoint copies of two \(r\)-element hyperedges intersecting in two vertices.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 5541031
zbMATH Keywords: Ramsey number
zbMATH Keywords: hypergraphs
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5541031