http://hdl.handle.net/2117/3198 2013-06-18T06:32:27Z http://hdl.handle.net/2117/8413 Title: Strong product of graphs: Geodetic and hull number and boundary-type sets Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María Luz 2010-07-27T09:58:31Z http://hdl.handle.net/2117/3013 Title: 4-labelings and grid embeddings of plane quadrangulations Authors: Barrière Figueroa, Eulalia; Huemer, Clemens 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. 2009-06-09T12:59:27Z