On a class of degenerate extremal graph problems

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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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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