Mostra el registre d'ítem simple
4-labelings and grid embeddings of plane quadrangulations
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 |
local.personalitzacitacio | true |
Fitxers d'aquest items
Aquest ítem apareix a les col·leccions següents
-
Reports de recerca [14]
-
Reports de recerca [403]
-
Reports de recerca [40]