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{\bf Yair Caro and Raphael Yuster}
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{\bf A Tur\'{a}n Type Problem Concerning the Powers of the Degrees of a Graph}
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For a graph $G$ whose degree sequence is $d_{1},\ldots ,d_{n}$, and for a
positive integer $p$, let $e_{p}(G)=\sum_{i=1}^{n}d_{i}^{p}$. For a fixed
graph $H$, let $t_{p}(n,H)$ denote the maximum value of $e_{p}(G)$ taken
over all graphs with $n$ vertices that do not contain $H$ as a subgraph.
Clearly, $t_{1}(n,H)$ is twice the Tur\'{a}n number of $H$. In this paper we
consider the case $p>1$. For some graphs $H$ we obtain exact results, for
some others we can obtain asymptotically tight upper and lower bounds, and
many interesting cases remain open.
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