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{\bf Oleg Pikhurko and Anusch Taraz}
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{\bf Degree Sequences of $F$-Free Graphs}
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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
generalization of the Tur\'an problem introduced by Caro and Yuster
[{\em Electronic J.\ Combin.} {\bf 7} (2000)].

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