{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:29Z","timestamp":1759063829009,"version":"3.41.2"},"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>In this note we prove the following theorem. For any three sets of points in the plane, each of $n\\ge 2$ points such that any three points (from the union of three sets) are not collinear and the convex hull of $3n$ points is monochromatic, there exists an integer $k\\in\\{1,2,\\dots,n-1\\}$ and an open half-plane containing exactly $k$ points from each set.<\/jats:p>","DOI":"10.37236\/2037","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:32:14Z","timestamp":1578713534000},"source":"Crossref","is-referenced-by-count":3,"title":["Balanced Line for a 3-Colored Point Set in the Plane"],"prefix":"10.37236","volume":"19","author":[{"given":"Sergey","family":"Bereg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikio","family":"Kano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,2,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:42:04Z","timestamp":1579300924000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/2037","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,2,7]]},"article-number":"P33"}}