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- Oswin Aichholzer, Clemens Huemer, Sarah Kappes, Bettina Speckmann, Csaba D. Tóth
- Graphs and Combinatorics
- 2006

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties… (More)

- Stefan Felsner, Clemens Huemer, Sarah Kappes, David Orden
- Discrete Mathematics & Theoretical Computer…
- 2010

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 quadrangu-lations (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… (More)

We provide binary labellings for the angles of quad-rangulations and plane Laman graphs which are in analogy with Schnyder labellings for triangulations

- Stefan Felsner, Sarah Kappes
- Order
- 2008

Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial already the three dimensional case has a rich structure with connections to Schnyder woods, planar graphs and… (More)

- Sarah Kappes
- 2006

Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial already the three dimensional case has a rich structure with connections to Schnyder woods, planar graphs and… (More)

Part of the authors introduced in [C. Huemer, S. Kappes, A binary labelling for plane Laman graphs and quadrangulations, in Proceedings of the 22nd European Workshop on Computational Geometry 83–86, 2006] a binary labeling for the angles of plane quadrangulations, similar to Schnyder labelings of the angles of plane triangulations since in both cases the… (More)

We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties… (More)

We present binary labelings for the angles of quadrangulations and plane Laman graphs, which are in analogy with Schnyder labelings for triangulations [W. Schnyder, Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, 1990] and imply a special tree decomposition for quadrangulations. In particular, we show how to embed quadrangula-tions on a 2-book, so that… (More)

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