Català   Castellano   English
 Empreu aquest identificador per citar o enllaçar aquest ítem: http://hdl.handle.net/2117/3013

Arxiu Descripció MidaFormat
 Títol: 4-labelings and grid embeddings of plane quadrangulations Autor: Barrière Figueroa, Eulalia ; Huemer, Clemens Data: 3-jun-2009 Tipus de document: External research report Resum: 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. URI: http://hdl.handle.net/2117/3013 Apareix a les col·leccions: COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions. Reports de recercaDCCG - Grup de recerca en geometria computacional, combinatoria i discreta. Reports de recercaDepartaments de Matemàtica Aplicada. Reports de recerca Comparteix: