On a class of degenerate extremal graph problems

Ralph J. Faudree, Miklós Simonovits

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Given a class ℒ of (so called "forbidden") graphs, ex (n, ℒ) denotes the maximum number of edges a graph G n of order n can have without containing subgraphs from ℒ. If ℒ contains bipartite graphs, then ex (n, ℒ)=O(n 2-c ) for some c>0, and the above problem is called degenerate. One important degenerate extremal problem is the case when C 2 k, a cycle of 2 k vertices, is forbidden. According to a theorem of P. Erdo{combining double acute accent}s, generalized by A. J. Bondy and M. Simonovits [32, ex (n, {C 2 k })=O(n 1+1/k ). In this paper we shall generalize this result and investigate some related questions.

Original languageEnglish
Pages (from-to)83-93
Number of pages11
JournalCombinatorica
Volume3
Issue number1
DOIs
Publication statusPublished - Mar 1 1983

Keywords

  • AMS subject classification (1980): 05C35

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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