## 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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag