On the Chromatic Number of Triangle-Free Graphs of Large Minimum Degree

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.

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Correspondence to Carsten Thomassen.

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Thomassen, C. On the Chromatic Number of Triangle-Free Graphs of Large Minimum Degree. Combinatorica 22, 591–596 (2002). https://doi.org/10.1007/s00493-002-0009-5

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AMS Subject Classification (2000):

  • 05C15
  • 05C35