On the Structure of Graphs with Bounded Clique Number

In this note, a structural result for maximal K r -free graphs is proven, which provides a simple proof of the Andrásfai–Erdős–Sós Theorem, saying that every K r -free graph with minimum degree \( \delta > {\left( {1 - \frac{1} {{r - \frac{4} {3}}}} \right)}n \) is (r−1)-colourable.

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Correspondence to Stephan Brandt.

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Brandt, S. Note. Combinatorica 23, 693–696 (2003).

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Mathematics Subject Classification (2000):

  • 05C35
  • 05C15
  • 05C75