A few remarks on Ramsey--Turán-type problems
type: Item
instance of: scholarly article
title: A few remarks on Ramsey--Turán-type problems
zbMATH Open document ID: 1029.05104
DOI: 10.1016/S0095-8956(02)00038-2
published in: Journal of Combinatorial Theory. Series B
publication date: 2003-08-25T00:00:00Z
review text: For fixed graph \(H\) and positive integer function \(f(n)\), the Ramsey-Turán number \(\text{RT}(n, H,f(n))\) is the maximum number of edges in a graph \(G\) of order \(n\) without having a copy of \(H\) and without \(f(n)\) independent vertices. Some improved bounds for some Ramsey-Turán numbers are proved. For example, it is shown for \(r > 2\), \(\text{RT}(n, K_4, n^{1 - 1/r}) < n^{2-1/r(r+1)}\). Results such as ``if \(H\) is a graph whose vertices can be partitioned into two sets each inducing an acyclic graph, then \(\text{RT}(n, H, ne^{-\omega(n)\sqrt{\ln n}}) = o(n^2)\), where \(\omega(n) \rightarrow \infty\) arbitrarily slowly with \(n\)'' are proved and used to give bounds for specific graphs.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1970679
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: Turán numbers
author: Benny Sudakov
reviewed by: Ralph Faudree
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970679