{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T15:30:35Z","timestamp":1768318235735,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $|A| &gt; f(n,2),$ 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 $l\\leq c n .$<\/jats:p>","DOI":"10.37236\/1323","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:55:16Z","timestamp":1578707716000},"source":"Crossref","is-referenced-by-count":6,"title":["On cycles in the coprime graph of integers"],"prefix":"10.37236","volume":"4","author":[{"given":"Paul","family":"Erd\u0151s","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabor N.","family":"Sarkozy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1996,12,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i2r8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v4i2r8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:14:41Z","timestamp":1579328081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v4i2r8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12,2]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,1,10]]}},"URL":"https:\/\/doi.org\/10.37236\/1323","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12,2]]},"article-number":"R8"}}