naa a22 4500 510783279 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0076-2 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0076-2 On the Ramsey-Turán numbers of graphs and hypergraphs [Elektronische Daten] [József Balogh, John Lenz] Let t be an integer, f(n) a function, and H a graph. Define the t-Ramsey-Turán number of H, RT t (n,H, f(n)), to be the maximum number of edges in an n-vertex, H-free graph G with α t (G) ≤ f(n), where α t (G) is the maximum number of vertices in a K t -free induced subgraph of G. Erdős, Hajnal, Simonovits, Sós and Szemerédi [6] posed several open questions about RT t (n,K s , o(n)), among them finding the minimum ℓ such that RT t (n,K t+ℓ , o(n)) = Ω(n 2), where it is easy to see that RT t (n,K t+1, o(n)) = o(n 2). In this paper, we answer this question by proving that RT t (n,K t+2, o(n)) = Ω(n 2); our constructions also imply several results on the Ramsey-Turán numbers of hypergraphs. Hebrew University Magnes Press, 2012 Balogh József Mathematics Department, University of Illinois, Urbana-Champaign, 61821, Urbana, IL, USA aut Lenz John Mathematics Department, University of Illinois, Urbana-Champaign, 61821, Urbana, IL, USA aut Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 45-68 0021-2172 194:1<45 2013 194 11856 https://doi.org/10.1007/s11856-012-0076-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0076-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balogh József Mathematics Department, University of Illinois, Urbana-Champaign, 61821, Urbana, IL, USA aut NATIONALLICENCE 700 1- Lenz John Mathematics Department, University of Illinois, Urbana-Champaign, 61821, Urbana, IL, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 45-68 0021-2172 194:1<45 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer