On a class of degenerate extremal graph problems

Ralph J. Faudree, M. Simonovits

Research output: Contribution to journalArticle

28 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 1983

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Extremal Graphs
Degenerate Problems
Extremal Problems
Graph in graph theory
Bipartite Graph
Acute
Subgraph
Denote
Cycle
Generalise
Theorem
Class

Keywords

  • AMS subject classification (1980): 05C35

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

On a class of degenerate extremal graph problems. / Faudree, Ralph J.; Simonovits, M.

In: Combinatorica, Vol. 3, No. 1, 03.1983, p. 83-93.

Research output: Contribution to journalArticle

Faudree, Ralph J. ; Simonovits, M. / On a class of degenerate extremal graph problems. In: Combinatorica. 1983 ; Vol. 3, No. 1. pp. 83-93.
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