On cycles in the coprime graph of integers

Paul Erdös, Gabor N. Sarkozy

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Article numberR8
Pages (from-to)1-11
Number of pages11
JournalElectronic Journal of Combinatorics
Volume4
Issue number2 R
Publication statusPublished - Dec 1 1997

ASJC Scopus subject areas

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

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