dc.contributor.author Barrière Figueroa, Eulalia dc.contributor.author Huemer, Clemens dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2009-06-09T12:59:27Z dc.date.available 2009-06-09T12:59:27Z dc.date.issued 2009-06-03 dc.identifier.uri http://hdl.handle.net/2117/3013 dc.description.abstract We show that each quadrangulation on $n$ vertices has a closed rectangle of influence drawing on the $(n-2) \times (n-2)$ grid. Further, we present a simple algorithm to obtain a straight-line drawing of a quadrangulation on the $\Big\lceil\frac{n}{2}\Big\rceil \times \Big\lceil\frac{3n}{4}\Big\rceil$ grid. This is not optimal but has the advantage over other existing algorithms that it is not needed to add edges to the quadrangulation to make it $4$-connected. The algorithm is based on angle labeling and simple face counting in regions analogous to Schnyder's grid embedding for triangulation. This extends previous results on book embeddings for quadrangulations from Felsner, Huemer, Kappes, and Orden (2008). Our approach also yields a representation of a quadrangulation as a pair of rectangulations with a curious property. dc.format.extent 14 p. dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Graph theory dc.subject.other embedding dc.subject.other labeling dc.subject.other quadrangulation dc.subject.other rectangle of influence dc.subject.other rectangulation dc.subject.other planar bipartite graph dc.title 4-labelings and grid embeddings of plane quadrangulations dc.type External research report dc.subject.lemac Grafs, Teoria de dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.contributor.group Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta dc.subject.ams Classificació AMS::05 Combinatorics::05C Graph theory dc.rights.access Open Access
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