On cycles in the coprime graph of integers

P. Erdős, 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 - 1997

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Coprime
Cycle
Integer
Graph in graph theory
Prime factor
Triangle
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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

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

In: Electronic Journal of Combinatorics, Vol. 4, No. 2 R, R8, 1997, p. 1-11.

Research output: Contribution to journalArticle

Erdős, P. ; Sarkozy, Gabor N. / On cycles in the coprime graph of integers. In: Electronic Journal of Combinatorics. 1997 ; Vol. 4, No. 2 R. pp. 1-11.
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