{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:18:05Z","timestamp":1775837885396,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We describe an explicit construction of triangle-free graphs with no independent sets of size $m$ and with $\\Omega(m^{3\/2})$ vertices, improving a sequence of previous constructions by various authors. As a byproduct we show that the maximum possible value of the Lov\u00e1sz $\\theta$-function of a graph on $n$ vertices with no independent set of size $3$ is $\\Theta(n^{1\/3})$, slightly  improving a result of Kashin and Konyagin who showed that this maximum is at least  $\\Omega(n^{1\/3}\/ \\log n)$ and at most $O(n^{1\/3})$. Our results imply that the maximum possible Euclidean norm of a sum of $n$ unit vectors  in $R^n$, so that among any three of them some two are orthogonal, is $\\Theta(n^{2\/3})$.<\/jats:p>","DOI":"10.37236\/1192","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:40:42Z","timestamp":1578638442000},"source":"Crossref","is-referenced-by-count":65,"title":["Explicit Ramsey graphs and orthonormal labelings"],"prefix":"10.37236","volume":"1","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1994,10,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v1i1r12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v1i1r12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:33:01Z","timestamp":1579339981000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v1i1r12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,10,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1994,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/1192","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,10,29]]},"article-number":"R12"}}