19 citations · 74 across the 43 of their papers we have counts for
6 papers · 1 filter
Balanced Islands in Two Colored Point Sets in the Plane
Oswin Aichholzer, Nieves Atienza, Ruy Fabila-Monroy +5
Let be a set of points in general position in the plane, of which are red and of which are blue. In this paper we prove that there exist: for every $α\in \left [ 0,…
Bishellable drawings of
Bernardo M. Ábrego, Oswin Aichholzer, Silvia Fernández-Merchant +6
The Harary--Hill conjecture, still open after more than 50 years, asserts that the crossing number of the complete graph is $ H(n) = \frac 1 4 \left\lfloor\frac{\mathstrut n}…
Representing Directed Trees as Straight Skeletons
Oswin Aichholzer, Therese Biedl, Thomas Hackl +4
The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple p…
Modem Illumination of Monotone Polygons
Oswin Aichholzer, Ruy Fabila-Monroy, David Flores-Peñaloza +3
We study a generalization of the classical problem of the illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a…
The Dual Diameter of Triangulations
Matias Korman, Stefan Langerman, Wolfgang Mulzer +3
Let $\Poly$ be a simple polygon with vertices. The \emph{dual graph} $\triang^*$ of a triangulation~$\triang$ of~$\Poly$ is the graph whose vertices correspond to the bounded f…
Evacuating Robots from a Disk Using Face-to-Face Communication
Jurek Czyzowicz, Konstantinos Georgiou, Evangelos Kranakis +3
Assume that two robots are located at the centre of a unit disk. Their goal is to evacuate from the disk through an exit at an unknown location on the boundary of the disk. At any…