http://hdl.handle.net/2117/3198 Thu, 20 Jun 2013 00:00:20 GMT 2013-06-20T00:00:20Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no 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 Tue, 27 Jul 2010 09:58:31 GMT http://hdl.handle.net/2117/8413 2010-07-27T09:58:31Z Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María Luz no Strong product, geodetic number, bull number, boundary-type sets 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. Tue, 09 Jun 2009 12:59:27 GMT http://hdl.handle.net/2117/3013 2009-06-09T12:59:27Z Barrière Figueroa, Eulalia; Huemer, Clemens no embedding, labeling, quadrangulation, rectangle of influence, rectangulation, planar bipartite graph 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.