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On a class of degenerate extremal graph problems

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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.

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Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Hungary

    Ralph J. Faudree

  2. Department of Mathematics, Memphis State University, 38152, Memphis, Tennessee, USA

    Ralph J. Faudree

  3. Department of Analysis I, Eötvös University, H-1088, Budapest, Hungary

    Miklós Simonovits

Authors
  1. Ralph J. Faudree
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  2. Miklós Simonovits
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Faudree, R.J., Simonovits, M. On a class of degenerate extremal graph problems. Combinatorica 3, 83–93 (1983). https://doi.org/10.1007/BF02579343

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