{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T01:13:37Z","timestamp":1773882817703,"version":"3.50.1"},"reference-count":2,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2000,2]]},"abstract":"<jats:p> Let X and Y be two disjoint sets of points in the plane such that |X|=|Y| and no three points of X \u222a Y are on the same line. Then we can draw an alternating Hamilton cycle on X\u222aY in the plane which passes through alternately points of X and those of Y, whose edges are straight-line segments, and which contains at most |X|-1 crossings. Our proof gives an O(n<jats:sup>2<\/jats:sup> log n) time algorithm for finding such an alternating Hamilton cycle, where n =|X|. Moreover we show that the above upper bound |X|-1 on crossing number is best possible for some configurations. <\/jats:p>","DOI":"10.1142\/s021819590000005x","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T08:18:55Z","timestamp":1052295535000},"page":"73-78","source":"Crossref","is-referenced-by-count":22,"title":["ALTERNATING HAMILTON CYCLES WITH MINIMUM NUMBER OF CROSSINGS IN THE PLANE"],"prefix":"10.1142","volume":"10","author":[{"given":"ATSUSHI","family":"KANEKO","sequence":"first","affiliation":[{"name":"Department of Computer Science and Communication Engineering, Kogakuin University, Shinjuku-ku, Tokyo 163-8677, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"KANO","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences, Ibaraki University, Hitachi 316-8511, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KIYOSHI","family":"YOSHIMOTO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Nihon Univeristy, Tokyo, 101-8308, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(90)90276-N"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(96)00124-X"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819590000005X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:29:51Z","timestamp":1565094591000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819590000005X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2]]},"references-count":2,"aliases":["10.1016\/s0218-1959(00)00005-x"],"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2000,2]]}},"alternative-id":["10.1142\/S021819590000005X"],"URL":"https:\/\/doi.org\/10.1142\/s021819590000005x","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,2]]}}}