Binary labelings for plane quadrangulations and their relatives

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one f...

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Detalles Bibliográficos
Autores: Felsner, Stefan, Huemer, Clemens|||0000-0001-7557-0823, Kappes, Sarah, Orden, David
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/8923
Acceso en línea:https://hdl.handle.net/2117/8923
Access Level:acceso abierto
Palabra clave:Combinatorial analysis
Graph theory
Schnyder labeling
Quadrangulation
Book embedding
Pseudo-triangulation
Laman graph
Anàlisi combinatòria
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Descripción
Sumario:Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our labeling resembles many of the properties of Schnyder's one for triangulations: Apart from being in bijection with tree decompositions, paths in these trees allow to define the regions of a vertex such that counting faces in them yields an algorithm for embedding the quadrangulation, in this case on a 2-book. Furthermore, as Schnyder labelings have been extended to 3-connected plane graphs, we are able to extend our labeling from quadrangulations to a larger class of 2-connected bipartite graphs.