On The Chromatic Number Of Pentagon-Free Graphs Of Large Minimum Degree

We prove that, for each fixed real number c > 0, the pentagon-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. A similar result holds for any other fixed odd cycle, except the triangle for which 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 Pentagon-Free Graphs Of Large Minimum Degree. Combinatorica 27, 241–243 (2007). https://doi.org/10.1007/s00493-007-0054-1

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Mathematics Subject Classification (2000):

  • 05C15