{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T07:32:53Z","timestamp":1769067173289,"version":"3.49.0"},"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 study the maximal number of triangulations that a planar set of $n$ points can have, and show that it is at most $30^n$. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of $43^n$ for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set.  Specifically, it can be used to derive new upper bounds for the number of planar graphs ($207.84^n$), spanning cycles ($O(68.67^n)$), spanning trees ($O(146.69^n)$), and cycle-free graphs ($O(164.17^n)$).<\/jats:p>","DOI":"10.37236\/557","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:51:58Z","timestamp":1578714718000},"source":"Crossref","is-referenced-by-count":32,"title":["Counting Triangulations of Planar Point Sets"],"prefix":"10.37236","volume":"18","author":[{"given":"Micha","family":"Sharir","sequence":"first","affiliation":[]},{"given":"Adam","family":"Sheffer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p70\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p70\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:14:53Z","timestamp":1579302893000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.37236\/557","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,31]]},"article-number":"P70"}}