{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:26Z","timestamp":1753893866301,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A semi-algebraic graph\u00a0$G = (V,E)$ is a graph where the vertices are points in $\\mathbb{R}^d$, and the edge set $E$ is defined by a semi-algebraic relation of constant complexity on $V$. In this note, we establish the following Ramsey-Tur\u00e1n theorem: for every integer $p\\geq 3$, every $K_{p}$-free semi-algebraic graph on $n$ vertices with independence number $o(n)$ has at most $\\frac{1}{2}\\left(1 - \\frac{1}{\\lceil p\/2\\rceil-1} + o(1) \\right)n^2$ edges. Here, the dependence on the complexity of the semi-algebraic relation is hidden in the $o(1)$ term.\u00a0 Moreover, we show that this bound is tight.<\/jats:p>","DOI":"10.37236\/7988","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:54:35Z","timestamp":1578668075000},"source":"Crossref","is-referenced-by-count":1,"title":["Ramsey-Tur\u00e1n Numbers for Semi-Algebraic Graphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Jacob","family":"Fox","sequence":"first","affiliation":[]},{"given":"J\u00e1nos","family":"Pach","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Suk","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,12,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p61\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p61\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:20:58Z","timestamp":1579234858000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p61"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7988","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,12,11]]},"article-number":"P4.61"}}