On the sum of the reciprocals of cycle lengths in sparse graphs

A. Gyárfás, H. J. Prömel, B. Voigt, E. Szemerédi

Research output: Contribution to journalArticle

Abstract

For a graph G let ℒ(G)=Σ{1/k contains a cycle of length k}. Erdo{combining double acute accent}s and Hajnal [1] introduced the real function f(α)=inf {ℒ (G)|E(G)|/|V(G)|≧α} and suggested to study its properties. Obviously f(1)=0. We prove f (k+1/k)≧(300 k log k)-1 for all sufficiently large k, showing that sparse graphs of large girth must contain many cycles of different lengths.

Original languageEnglish
Pages (from-to)41-52
Number of pages12
JournalCombinatorica
Volume5
Issue number1
DOIs
Publication statusPublished - Mar 1 1985

Keywords

  • AMS subject classification (1980): 05C38, 05C05

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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