6 papers
Holes in Convex and Simple Drawings
Helena Bergold, Joachim Orthaber, Manfred Scheucher +1
Gons and holes in point sets have been extensively studied in the literature. For simple drawings of the complete graph a generalization of the ErdÅs--Szekeres theorem is known an…
Plane Hamiltonian Cycles in Convex Drawings
Helena Bergold, Stefan Felsner, Meghana M. Reddy +2
A conjecture by Rafla from 1988 asserts that every simple drawing of the complete graph admits a plane Hamiltonian cycle. It turned out that already the existence of much sim…
Garment numbers of bi-colored point sets in the plane
Oswin Aichholzer, Helena Bergold, Simon D. Fink +3
We consider colored variants of a class of geometric-combinatorial questions on -gons and empty -gons that have been started around 1935 by ErdÅs and Szekeres. In our settin…
Investigating Simple Drawings of using SAT
Helena Bergold, Manfred Scheucher
We present a SAT framework which allows to investigate properties of simple drawings of the complete graph using the power of AI. In contrast to classic imperative programmin…
On Triangular Separation of Bichromatic Point Sets
Helena Bergold, Arun Kumar Das, Robert Lauff +3
We address the problem of computing the minimum number of triangles to separate a set of blue points from a set of red points in . A set of triangles is a \emph{separ…
Signotopes with few plus signs
Helena Bergold, Lukas Egeling, Hung. P. Hoang
Arrangements of pseudohyperplanes are widely studied in computational geometry. A rich subclass of pseudohyerplane arrangements, which has gained more attention in recent years, is…