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In this paper we consider planar L-shaped embeddings of trees in point sets, that is, planar drawings where the vertices are mapped to a subset of the given points and where every edge consists of two axis-aligned line segments. We investigate the minimum number m, such that any n vertex tree with maximum degree 4 admits a planar L-shaped embedding in any… (More)

- Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, Manfred Scheucher
- Symposium on Computational Geometry
- 2016

A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free… (More)

- Stefan Felsner, Manfred Scheucher
- ArXiv
- 2017

A pseudocircle is a simple closed curve on the sphere or in the plane. The study of arrangements of pseudocircles was initiated by Grünbaum, who defined them as collections of simple closed curves that pairwise intersect in exactly two crossings. Grünbaum conjectured that the number of triangular cells p3 in digon-free arrangements of n pairwise… (More)

- Oswin Aichholzer, Martin Balko, +5 authors Birgit Vogtenhuber
- Symposium on Computational Geometry
- 2017

Let P be a finite set of points in the plane in general position, that is, no three points of P are on a common line. We say that a set H of five points from P is a 5-hole in P if H is the vertex set of a convex 5-gon containing no other points of P . For a positive integer n, let h5(n) be the minimum number of 5-holes among all sets of n points in the… (More)

- Yung-Hsiang Lien, Giovanni Barontini, Manfred Scheucher, Marcus Mergenthaler, Jonathan Goldwin, E. A. Hinds
- Nature communications
- 2016

It is usually considered that the spectrum of an optical cavity coupled to an atomic medium does not exhibit a normal-mode splitting unless the system satisfies the strong coupling condition, meaning the Rabi frequency of the coherent coupling exceeds the decay rates of atom and cavity excitations. Here we show that this need not be the case, but depends on… (More)

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