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Combinatorica

, Volume 3, Issue 1, pp 83–93 | Cite as

On a class of degenerate extremal graph problems

  • Ralph J. Faudree
  • Miklós Simonovits
Article

Abstract

Given a class ℒ of (so called “forbidden”) graphs, ex (n, ℒ) denotes the maximum number of edges a graphG n of ordern can have without containing subgraphs from ℒ. If ℒ contains bipartite graphs, then ex (n, ℒ)=O(n 2−c ) for somec>0, and the above problem is calleddegenerate. One important degenerate extremal problem is the case whenC 2k , a cycle of 2k vertices, is forbidden. According to a theorem of P. Erdős, generalized by A. J. Bondy and M. Simonovits [32, ex (n, {C 2k })=O(n 1+1/k ). In this paper we shall generalize this result and investigate some related questions.

AMS subject classification (1980)

05 C 35 

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Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • Ralph J. Faudree
    • 1
    • 2
  • Miklós Simonovits
    • 3
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesHungary
  2. 2.Department of MathematicsMemphis State UniversityMemphisUSA
  3. 3.Department of Analysis IEötvös UniversityBudapestHungary

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