### 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 1983 |

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### Keywords

- AMS subject classification (1980): 05C35

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Combinatorica*,

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

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

Research output: Contribution to journal › Article

*Combinatorica*, vol. 3, no. 1, pp. 83-93. https://doi.org/10.1007/BF02579343

}

TY - JOUR

T1 - On a class of degenerate extremal graph problems

AU - Faudree, Ralph J.

AU - Simonovits, M.

PY - 1983/3

Y1 - 1983/3

N2 - 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.

AB - 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.

KW - AMS subject classification (1980): 05C35

UR - http://www.scopus.com/inward/record.url?scp=51249185516&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51249185516&partnerID=8YFLogxK

U2 - 10.1007/BF02579343

DO - 10.1007/BF02579343

M3 - Article

VL - 3

SP - 83

EP - 93

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -