On Turán’s theorem for sparse graphs


For a graphG withn vertices and average valencyt, Turán’s theorem yields the inequalityαn/(t+1) whereα denotes the maximum size of an independent set inG. We improve this bound for graphs containing no large cliques.

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Ajtai, M., Erdős, P., Komlós, J. et al. On Turán’s theorem for sparse graphs. Combinatorica 1, 313–317 (1981). https://doi.org/10.1007/BF02579451

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 55