Note: The binding number of a graph and its cliques
Discrete Applied Mathematics
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In this note, a structural result for maximal Kr-free graphs is proven, which provides a simple proof of the Andrásfai–Erdős–Sós Theorem, saying that every Kr-free graph with minimum degree $$\delta {\left( {1 - \frac{1}{{r - \frac{4}{3}}}} \right)}n$$ is (r−1)-colourable.