Thomassen, Carsten On the chromatic number of triangle-free graphs of large minimum degree. (English) Zbl 1026.05042 Combinatorica 22, No. 4, 591-596 (2002). It is proved that, for each real number \(c>1/3\), the triangle-free graphs with minimum degree at least \(cn\) (\(n\) the number of vertices) have bounded chromatic number. This settles a longstanding open problem of Erdős and Simonovits who showed that there is no such result for \(c<1/3\). Reviewer: Miklós Ruszinkó (Budapest) Cited in 4 ReviewsCited in 22 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05C35 Extremal problems in graph theory Keywords:triangle-free graphs; chromatic number PDFBibTeX XMLCite \textit{C. Thomassen}, Combinatorica 22, No. 4, 591--596 (2002; Zbl 1026.05042) Full Text: DOI Link