Lower bounds for hypergraph Ramsey numbers
type: Item
instance of: scholarly article
title: Lower bounds for hypergraph Ramsey numbers
zbMATH Open document ID: 0828.05041
DOI: 10.1016/0166-218X(94)00167-C
author: H. L. Abbott
author: M. J. Smuga-Otto
published in: Discrete Applied Mathematics
publication date: 1995-12-18T00:00:00Z
review text: For \(m_1, m_2,\dots, m_k\) with \(m_i\geq r\), \(R(m_1,\dots, m_k; r)\) denotes the least integer \(n\) such that when \(f\) is any \(k\)- coloring of the \(r\)-subsets of an \(n\)-set there is an index \(i\) and an \(m_i\) subset such that all of its \(r\)-subsets are assigned the \(i\)th color. If \(m_1= m_2=\dots = m_k= m\), we write \(R_k(m; r)\) for \(R(m_1,\dots, m_k; r)\). The main result of this paper is: For \(k\geq 2\), \(h\geq 2\), \(m\geq r\), \(r\geq 3\) and \(2\leq q< r\), we have \(R(m, R_k(r; q),(r- 1)^h+ 1; r)> (R_k(m; q)- 1)^h\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 790498
zbMATH Keywords: hypergraph Ramsey numbers
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: Some remarks on the theory of graphs
cites work: Ramsey-type theorems
cites work: Partition relations for cardinal numbers
cites work: Combinatorial Theorems on Classifications of Subsets of a Given Set
cites work: Q3770573
cites work: Q3138966
description: scientific article; zbMATH DE number 790498