We prove that, for each fixed real number c > 1/3, the triangle-free graphs of minimum degree at least cn (where n is the number of vertices) have bounded chromatic number. This problem was raised by Erdős and Simonovits in 1973 who pointed out that there is no such result for c < 1/3.
On the Chromatic Number of Triangle-Free Graphs of Large Minimum Degree
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- Volume 22, pages 591–596, (2002)
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