Abstract We prove Turán-type theorems for two related Ramsey problems raised by Bollobás and Fox Sudakov. First, t ≥ 3, we show that any two-colouring of the complete graph on n vertices is δ -far from being monochromatic contains an unavoidable t-colouring when ≫ −1/ , where -colouring a clique order 2 in which one colour forms either or disjoint cliques . Next, tournament transitive t-tournam...

Zoltán Füredi1 Alfréd Rényi Institute Hungarian Academy of Sciences Budapest, P.O.Box 127, Hungary, H-1364, [email protected] and Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, USA [email protected] Lale Özkahya Department of Mathematics Iowa State University Ames, IA 50011, USA [email protected] Abstract One of the central problems of extremal...