### 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 |
---|---|

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 - Dec 1 1997 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'On cycles in the coprime graph of integers'. Together they form a unique fingerprint.

## Cite this

Erdös, P., & Sarkozy, G. N. (1997). On cycles in the coprime graph of integers.

*Electronic Journal of Combinatorics*,*4*(2 R), 1-11. [R8].