{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:28Z","timestamp":1761611188929},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,10]]},"abstract":"<jats:p> In a convex drawing of a plane graph G, every facial cycle of G is drawn as a convex polygon. A polygon for the outer facial cycle is called an outer convex polygon. A necessary and sufficient condition for a plane graph G to have a convex drawing is known. However, it has not been known how many apices of an outer convex polygon are necessary for G to have a convex drawing. In this paper, we show that the minimum number of apices of an outer convex polygon necessary for G to have a convex drawing is, in effect, equal to the number of leaves in a triconnected component decomposition tree of a new graph constructed from G, and that a convex drawing of G having the minimum number of apices can be found in linear time. <\/jats:p>","DOI":"10.1142\/s0129054106004297","type":"journal-article","created":{"date-parts":[[2006,9,18]],"date-time":"2006-09-18T12:04:43Z","timestamp":1158581083000},"page":"1115-1127","source":"Crossref","is-referenced-by-count":15,"title":["CONVEX DRAWINGS OF PLANE GRAPHS OF MINIMUM OUTER APICES"],"prefix":"10.1142","volume":"17","author":[{"given":"KAZUYUKI","family":"MIURA","sequence":"first","affiliation":[{"name":"Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MACHIKO","family":"AZUMA","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TAKAO","family":"NISHIZEKI","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","unstructured":"N.\u00a0Chiba, T.\u00a0Yamanouchi and T.\u00a0Nishizeki, Progress in Graph Theory, eds. J. A.\u00a0Bondy and U. S. R.\u00a0Murty (Academic Press, 1984)\u00a0pp. 153\u2013173."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195997000144"},{"key":"rf3","volume-title":"Graph Drawing","author":"Di Battista G.","year":"1999"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s004539900017"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/0202012"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44969-8"},{"key":"rf7","first-page":"117","volume":"16","author":"Miura K.","journal-title":"International Journal of Fundations of Computer Science"},{"key":"rf8","volume-title":"Planar Graphs: Theory and Algorithms","author":"Nishizeki T.","year":"1988"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/5648"},{"key":"rf11","unstructured":"C.\u00a0Thomassen, Progress in Graph Theory, eds. J. A.\u00a0Bondy and U. S. R.\u00a0Murty (Academic Press, 1984)\u00a0pp. 43\u201369."}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054106004297","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:40:42Z","timestamp":1565138442000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054106004297"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":10,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1142\/S0129054106004297"],"URL":"https:\/\/doi.org\/10.1142\/s0129054106004297","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]}}}