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

الأصل · EN

For a graph G whose degree sequence is d₁,..., dₙ, and for a positive integer p, let eₚ(G)=∑ᵢ₌₁ⁿdᵢᵖ. For a fixed graph H, let tₚ(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, t₁(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.