{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:03Z","timestamp":1753893783124,"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>The rectilinear crossing number of a graph $G$ is the minimum number of edge crossings that can occur in any drawing of $G$ in which the edges are straight line segments and no three vertices are collinear. This number has been known for $G=K_n$ if $n \\leq 9$.  Using a combinatorial argument we show that for $n=10$ the number is 62.  <\/jats:p>","DOI":"10.37236\/1567","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:08:53Z","timestamp":1578690533000},"source":"Crossref","is-referenced-by-count":12,"title":["The Rectilinear Crossing Number of $K_{10}$ is $62$"],"prefix":"10.37236","volume":"8","author":[{"given":"Alex","family":"Brodsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephane","family":"Durocher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ellen","family":"Gethner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2001,4,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:18:15Z","timestamp":1579306695000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,4,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1567","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,4,9]]},"article-number":"R23"}}