For a graph G whose degree sequence is d1, ..., dn, and for a positive integer p, let ep(G) = ∑i=1 n dip. For a fixed graph H, let t p(n,H) denote the maximum value of ep(G) taken over all graphs with n vertices that do not contain H as a subgraph. Clearly, t 1(n,H) is twice the Turán 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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics