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In this paper we give a brief survey of existing lower and upper bounds on the rank of the 3-dimensional rigidity matroid of a graph and introduce a new upper bound, which may lead to the desired good characterization. <\/jats:p>","DOI":"10.1142\/s0218195906002117","type":"journal-article","created":{"date-parts":[[2006,11,3]],"date-time":"2006-11-03T11:57:15Z","timestamp":1162555035000},"page":"415-429","source":"Crossref","is-referenced-by-count":12,"title":["ON THE RANK FUNCTION OF THE 3-DIMENSIONAL RIGIDITY MATROID"],"prefix":"10.1142","volume":"16","author":[{"given":"BILL","family":"JACKSON","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, England"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"TIBOR","family":"JORD\u00c1N","sequence":"additional","affiliation":[{"name":"Department of Operations Research, E\u00f6tv\u00f6s University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1\/C, 1117 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22143-3"},{"key":"rf2","volume-title":"Distance Geometry and Molecular Conformation","author":"Crippen G. 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