Monochromatic coverings and tree Ramsey numbers
type: Item
instance of: scholarly article
title: Monochromatic coverings and tree Ramsey numbers
zbMATH Open document ID: 0795.05096
DOI: 10.1016/0012-365X(94)90179-1
author: Zsolt Tuza
published in: Discrete Mathematics
publication date: 1994-05-05T00:00:00Z
review text: The main result of this paper is the following Ramsey type theorem. Let \(k=3\) or 4 and let \(n\) be a natural number not divisible by \(k-1\). Consider any edge \(k\)-coloring of the complete graph \(K_ p\) where \(p=(k-1) (n-1)+2\). Then \(K_ p\) admits \(k-1\) monochromatic connected subgraphs \(G_ 1, \dots, G_{k-1}\) so that \[ | V (G_ 1) | \geq n+1 \text{ and } V(G_ 1) \cup V(G_ 2) \cup \cdots \cup V (G_{k- 1})=V (K_ p). \] Some partial results are also obtained for \(k>4\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 562682
zbMATH Keywords: coverings
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: complete graph
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: Q5612352
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cites work: Multipartite Turán problem for connected graphs and hypergraphs
full work available at URL: 0012-365x(94)90179-1
OpenAlex ID: W1991179333
description: scientific article; zbMATH DE number 562682