Highly Influenced

@article{Pikhurko2005DegreeSO, title={Degree Sequences of F-Free Graphs}, author={Oleg Pikhurko and Anusch Taraz}, journal={Electr. J. Comb.}, year={2005}, volume={12} }

- Published 2005 in Electr. J. Comb.

Let F be a fixed graph of chromatic number r + 1. We prove that for all large n the degree sequence of any F -free graph of order n is, in a sense, close to being dominated by the degree sequence of some r-partite graph. We present two different proofs: one goes via the Regularity Lemma and the other uses a more direct counting argument. Although the latter proof is longer, it gives better estimates and allows F to grow with n. As an application of our theorem, we present new results on the… CONTINUE READING