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- Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Ferran Hurtado, Hannes Krasser, Birgit Vogtenhuber
- Graphs and Combinatorics
- 2007

- Oswin Aichholzer, Sergio Cabello, +5 authors David R. Wood
- Discrete Mathematics & Theoretical Computer…
- 2010

A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V. We study the following extremal problem for geometric graphs: How many arbitrary edges can be removed from a complete geometric graph with n vertices such that the remaining graph… (More)

- Oswin Aichholzer, Franz Aurenhammer, Clemens Huemer, Hannes Krasser
- EuroCG
- 2005

Let T S be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph T S where two members T and T of T S are adjacent if T intersects T only in points of S or in common edges. We prove that the diameter of T S is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the… (More)

- Clemens Huemer, Ferran Hurtado, Marc Noy, Elsa Omaña-Pulido
- Discrete Applied Mathematics
- 2009

- Oswin Aichholzer, Sergey Bereg, +10 authors David R. Wood
- Comput. Geom.
- 2008

This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect match-ings M and M of the same set of n points, for some k ∈ O(log n), there is a sequence of perfect matchings M = M 0 , M 1 ,. .. , M… (More)

- Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Ferran Hurtado, Birgit Vogtenhuber
- SIAM J. Discrete Math.
- 2010

We consider a variation of a problem stated by Erd˝ os and Szekeres in 1935 about the existence of a number f ES (k) such that any set S of at least f ES (k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned… (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)

- Alfredo García Olaverri, Ferran Hurtado, Clemens Huemer, Javier Tejel, Pavel Valtr
- Comput. Geom.
- 2009

- 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)

- Oswin Aichholzer, Clemens Huemer, Hannes Krasser
- Comput. Geom.
- 2008

Problem 50 in the Open Problems Project of the computational geometry community asks whether any triangulation on a point set in the plane contains a pointed spanning tree as a subgraph. We provide a counterexample. As a consequence we show that there exist triangulations which require a linear number of edge flips to become Hamiltonian.