{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:29Z","timestamp":1761611189132},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","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>A convex grid drawing of a plane graph G is a drawing of G on the plane such that all vertices of G are put on grid points, all edges are drawn as straight-line segments without any edge-intersection, and every face boundary is a convex polygon. In this paper we give a linear-time algorithm for finding a convex grid drawing of every 4-connected plane graph G with four or more vertices on the outer face. The size of the drawing satisfies W + H \u2264 n - 1, where n is the number of vertices of G, W is the width and H is the height of the grid drawing. Thus the area W \u00b7 H is at most \u2308(n - 1)\/2\u2309 \u00b7 \u230a(n - 1)\/2\u230b. Our bounds on the sizes are optimal in a sense that there exist an infinite number of 4-connected plane graphs whose convex drawings need grids such that W + H = n - 1 and W \u00b7 H = \u2308(n - 1)\/2\u2309 \u00b7 \u230a(n - 1)\/2\u230b.<\/jats:p>","DOI":"10.1142\/s012905410600425x","type":"journal-article","created":{"date-parts":[[2006,9,18]],"date-time":"2006-09-18T12:04:43Z","timestamp":1158581083000},"page":"1031-1060","source":"Crossref","is-referenced-by-count":10,"title":["CONVEX GRID DRAWINGS OF FOUR-CONNECTED PLANE GRAPHS"],"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":"SHIN-ICHI","family":"NAKANO","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, Gunma University, Kiryu 376-8515, 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","volume-title":"Graph Drawing","author":"Di Battista G.","year":"1999"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195997000144"},{"key":"rf3","first-page":"29","volume":"10","author":"Chrobak M.","journal-title":"Computational Geometry: Theory and Applications"},{"key":"rf4","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF00264230","volume":"22","author":"Chiba N.","journal-title":"Acta Inform."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(95)00020-D"},{"key":"rf6","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":"rf7","first-page":"229","volume":"11","author":"F\u00e1ry I.","journal-title":"Acta. Sci. Math. Szeged"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02122694"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009290"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02086606"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(95)00257-X"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-001-0004-4"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/5648"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(97)00083-5"},{"key":"rf20","first-page":"743","volume":"13","author":"Tutte W. T.","journal-title":"Proc. London Math. Soc."}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S012905410600425X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T13:51:26Z","timestamp":1707227486000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012905410600425X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":15,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1142\/S012905410600425X"],"URL":"https:\/\/doi.org\/10.1142\/s012905410600425x","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]}}}