On graphs with subgraphs having large independence numbers

: Let G be a graph on n vertices in which every induced subgraph on s = log3 n vertices has an independent set of size at least t = log n. What is the largest q = q(n) so that every such G must contain an independent set of size at least q? This is one of the several related questions raised by Erd˝os and Hajnal. We show that q(n) = (log2 n/log log n), investigate Contract grant sponsor: Israel Science Foundation (to N.A.); Contract grant sponsor: USA-Israeli BSF grant (to N.A.); Contract grant sponsor: Hermann Minkowski Minerva Center for Geometry (to N.A.); Contract grant sponsor: NSF CAREER award (to B.S.); Contract grant number: DMS-0546523; Contract grant sponsor: NSF (to B.S.); Contract grant number: DMS-0355497; Contract grant sponsor: Alfred P. Sloan fellowship; Contract grant sponsor: State of New Jersey. Journal of Graph Theory © 2007 Wiley Periodicals, Inc. 149 

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: Noga Alon, Benny Sudakov
• Keywords: Grant Sponsor, Independent Set, JGT 2007, USA-Israeli BSF Grant