Felsner, Stefan and Huemer, Clemens and Kappes, Sarah and Orden, David - Binary Labelings for Plane Quadrangulations and their Relatives

dmtcs:475 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, Vol. 12 no. 3
Binary Labelings for Plane Quadrangulations and their Relatives

Authors: Felsner, Stefan and Huemer, Clemens and Kappes, Sarah and Orden, David

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.


Source : oai:HAL:hal-00993747v1
Volume: Vol. 12 no. 3
Section: Graph and Algorithms
Published on: January 1, 2011
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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