Abstract
We consider the structure of Kr-free graphs with large minimum degree, and show that such graphs with minimum degree δ>(2r − 5)n/(2r − 3) are homomorphic to the join Kr − 3∨H, where H is a triangle-free graph. In particular this allows us to generalize results from triangle-free graphs and show that Kr-free graphs with such a minimum degree have chromatic number at most r +1. We also consider the minimum-degree thresholds for related properties. Copyright © 2010 John Wiley & Sons, Ltd. 66:319-331, 2011
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