DSpace Collection:
http://hdl.handle.net/2117/3198
Wed, 17 Sep 2014 11:43:17 GMT2014-09-17T11:43:17Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoStrong product of graphs: Geodetic and hull number and boundary-type sets
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 LuzTue, 27 Jul 2010 09:58:31 GMThttp://hdl.handle.net/2117/84132010-07-27T09:58:31ZCáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas González, María LuznoStrong product, geodetic number, bull number, boundary-type sets4-labelings and grid embeddings of plane quadrangulations
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 GMThttp://hdl.handle.net/2117/30132009-06-09T12:59:27ZBarrière Figueroa, Eulalia; Huemer, Clemensnoembedding, labeling, quadrangulation, rectangle of influence, rectangulation, planar bipartite graphWe 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.