### 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 [3_{2}, ex (n, {C_{ 2 k} })=O(n^{ 1+1/k} ). In this paper we shall generalize this result and investigate some related questions.

Original language | English |
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Pages (from-to) | 83-93 |

Number of pages | 11 |

Journal | Combinatorica |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1 1983 |

### Keywords

- AMS subject classification (1980): 05C35

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

Faudree, R. J., & Simonovits, M. (1983). On a class of degenerate extremal graph problems.

*Combinatorica*,*3*(1), 83-93. https://doi.org/10.1007/BF02579343