Degree Sequences of F-Free Graphs

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