A Turán type problem concerning the powers of the degrees of a graph

Yair Caro; Raphael Yuster

doi:10.37236/1525

A Turán type problem concerning the powers of the degrees of a graph

Yair Caro
, Raphael Yuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a graph G whose degree sequence is d₁, ..., d_n, and for a positive integer p, let e_p(G) = ∑_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 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.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Electronic Journal of Combinatorics
Volume	7
Issue number	1 R
DOIs	https://doi.org/10.37236/1525
State	Published - 2000

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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title = "A Tur{\'a}n type problem concerning the powers of the degrees of a graph",

abstract = "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 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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AU - Yuster, Raphael

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AB - 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.

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ER -

A Turán type problem concerning the powers of the degrees of a graph

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