### Abstract

The set of different cycle lengths of a graph G is denoted by C(G). We study how the distribution of C(G) depends on the minimum degree of G. We prove two results indicating that C(G) is dense in some sense. These results lead to the solution of a conjecture of Erdös and Hajnal stating that for suitable positive constants a, b the following holds: (Formula Presented.) where δ(G) denotes the minimum degree of G.

Original language | English |
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Pages (from-to) | 441-462 |

Number of pages | 22 |

Journal | Journal of Graph Theory |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1984 |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

*8*(4), 441-462. https://doi.org/10.1002/jgt.3190080402

**On the distribution of cycle lengths in graphs.** / Gyárfás, A.; Komlós, J.; Szemerédi, E.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 8, no. 4, pp. 441-462. https://doi.org/10.1002/jgt.3190080402

}

TY - JOUR

T1 - On the distribution of cycle lengths in graphs

AU - Gyárfás, A.

AU - Komlós, J.

AU - Szemerédi, E.

PY - 1984

Y1 - 1984

N2 - The set of different cycle lengths of a graph G is denoted by C(G). We study how the distribution of C(G) depends on the minimum degree of G. We prove two results indicating that C(G) is dense in some sense. These results lead to the solution of a conjecture of Erdös and Hajnal stating that for suitable positive constants a, b the following holds: (Formula Presented.) where δ(G) denotes the minimum degree of G.

AB - The set of different cycle lengths of a graph G is denoted by C(G). We study how the distribution of C(G) depends on the minimum degree of G. We prove two results indicating that C(G) is dense in some sense. These results lead to the solution of a conjecture of Erdös and Hajnal stating that for suitable positive constants a, b the following holds: (Formula Presented.) where δ(G) denotes the minimum degree of G.

UR - http://www.scopus.com/inward/record.url?scp=84986535296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986535296&partnerID=8YFLogxK

U2 - 10.1002/jgt.3190080402

DO - 10.1002/jgt.3190080402

M3 - Article

VL - 8

SP - 441

EP - 462

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 4

ER -