A Turán Type Problem Concerning the Powers of the Degrees of a Graph (revised)

Details A Turán Type Problem Concerning the Powers of the Degrees of a Graph (revised) A Turán Type Problem Concerning the Powers of the Degrees of a Graph (revised)

2004-01-28

arxiv.org/abs/math/0401398v1

The Electronic Journal of Combinatorics 7 (2000), #R47

Mathematics

Combinatorics

14 Pages

Scientific paper

For a graph $G$ whose degree sequence is $d_{1},..., d_{n}$, 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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