### Abstract

In this paper we study cycles in the coprime graph of integers. We denote by f(n, k) the number of positive integers m ≤ n with a prime factor among the first k primes. We show that there exists a constant c such that if A ⊂ {1,2,..., n} with |A| > f(n, 2) (if 6|n then f(n, 2) = 2/3n), then the coprime graph induced by A not only contains a triangle, but also a cycle of length 21 + 1 for every positive integer l ≤ cn.

Original language | English |
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Article number | R8 |

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Electronic Journal of Combinatorics |

Volume | 4 |

Issue number | 2 R |

Publication status | Published - 1997 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Electronic Journal of Combinatorics*,

*4*(2 R), 1-11. [R8].

**On cycles in the coprime graph of integers.** / Erdős, P.; Sarkozy, Gabor N.

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 4, no. 2 R, R8, pp. 1-11.

}

TY - JOUR

T1 - On cycles in the coprime graph of integers

AU - Erdős, P.

AU - Sarkozy, Gabor N.

PY - 1997

Y1 - 1997

N2 - In this paper we study cycles in the coprime graph of integers. We denote by f(n, k) the number of positive integers m ≤ n with a prime factor among the first k primes. We show that there exists a constant c such that if A ⊂ {1,2,..., n} with |A| > f(n, 2) (if 6|n then f(n, 2) = 2/3n), then the coprime graph induced by A not only contains a triangle, but also a cycle of length 21 + 1 for every positive integer l ≤ cn.

AB - In this paper we study cycles in the coprime graph of integers. We denote by f(n, k) the number of positive integers m ≤ n with a prime factor among the first k primes. We show that there exists a constant c such that if A ⊂ {1,2,..., n} with |A| > f(n, 2) (if 6|n then f(n, 2) = 2/3n), then the coprime graph induced by A not only contains a triangle, but also a cycle of length 21 + 1 for every positive integer l ≤ cn.

UR - http://www.scopus.com/inward/record.url?scp=4243915292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243915292&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4243915292

VL - 4

SP - 1

EP - 11

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 2 R

M1 - R8

ER -