Carsten Thomassen proved in 1999 the conjecture made by Erdos and Simonovits in 1973 that for every c greater than 1/3, the triangle-free graphs of minimum degree at least cn have bounded chromatic number. There is no such result if c is less than 1/3. In collaboration with Adrian Bondy and Stephan Thomasse at Universite Claude Bernard,Lyon, Carsten Thomassen studies density conditions implying triangles in graphs.