Moments of graphs in monotone families

Zoltán Füredi, André Kündgen

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The kth moment of the degree sequence d 1 ≥ d 2 ≥... d n of a graph G is μ k(G) = 1/nΣ d i k. We give asymptotically sharp bounds for μ k(G) when G is in a monotone family. We use these results for the case k = 2 to improve a result of Pach, Spencer, and Tóth [15]. We answer a question of Erd″os [9] by determining the maximum variance μ 2(G) - μ 1 2(G) of the degree sequence when G is a triangle-free n-vertex graph.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalJournal of Graph Theory
Volume51
Issue number1
DOIs
Publication statusPublished - Jan 1 2006

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Keywords

  • Degree sequence
  • Moments
  • Monotone graph family
  • Optimization

ASJC Scopus subject areas

  • Geometry and Topology

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