Geodesic
On cycles in the coprime graph of integers
The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2
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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. (If $6|n,$ then $f(n,2)={{2n}\over {3}} $.) We show that there exists a constant $c$ such that if $A\subset \{1, 2, \ldots , n\}$ with $|A| > f(n,2),$ then the coprime graph induced by $A$ not only contains a triangle, but also a cycle of length $2 l + 1$ for every positive integer $l\leq c n .$
DOI : 10.37236/1323
Classification : 11B75, 05C38
Mots-clés : cycles, coprime graph of integers 
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     author = {Paul Erd\H{o}s and Gabor N. Sarkozy},
     title = {On cycles in the coprime graph of integers},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {2},
     doi = {10.37236/1323},
     zbl = {0932.11013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1323/}
}
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Paul Erdős; Gabor N. Sarkozy. On cycles in the coprime graph of integers. The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2. doi: 10.37236/1323

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