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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 980.10616

**Autor: ** Erdös, Paul; Sarkozy, Gabor N.

**Title: ** On cycles in the coprime graph of integers. (In English)

**Source: ** Electron. J. Comb. 4, No.2, Research paper R8, 11 p. (1997).

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

**Classif.: ** * 11B75 Combinatorial number theory

05C38 Paths and cycles

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