{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T06:49:18Z","timestamp":1765176558338,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $n \\geq 4$ be even. It is shown that every set $S$ of $n$ points in the plane can be connected by a (possibly self-intersecting) spanning tour (Hamiltonian cycle) consisting of $n$ straight-line edges such that the angle between any two consecutive edges is at most $2\\pi\/3$. For $n=4$ and $6$, this statement is tight. It is also shown that every even-element point set $S$ can be partitioned\u00a0 into at most two subsets, $S_1$ and $S_2$, each admitting a spanning tour with no angle larger than $\\pi\/2$. Fekete and Woeginger conjectured that for sufficiently large even $n$, every $n$-element set admits such a spanning tour. We confirm this conjecture for point sets in convex position. A much stronger result holds for large point sets randomly and uniformly selected from an open region bounded by finitely many rectifiable curves: for any $\\epsilon&gt;0$, these sets almost surely admit a spanning tour with no angle larger than $\\epsilon$.<\/jats:p>","DOI":"10.37236\/2356","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:27:48Z","timestamp":1578713268000},"source":"Crossref","is-referenced-by-count":9,"title":["Drawing Hamiltonian Cycles with no Large Angles"],"prefix":"10.37236","volume":"19","author":[{"given":"Adrian","family":"Dumitrescu","sequence":"first","affiliation":[]},{"given":"J\u00e1nos","family":"Pach","sequence":"additional","affiliation":[]},{"given":"G\u00e9za","family":"T\u00f3th","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,6,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:35:30Z","timestamp":1579300530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i2p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2356","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,6,6]]},"article-number":"P31"}}