2 citations · 3 across the 3 of their papers we have counts for
7 papers
Arrangements of orthogonal circles with many intersections
Sarah Carmesin, André Schulz
An arrangement of circles in which circles intersect only in angles of is called an \emph{arrangement of orthogonal circles}. We show that in the case that no two circles are…
Augmenting Geometric Graphs with Matchings
Alexander Pilz, Jonathan Rollin, Lena Schlipf +1
We study noncrossing geometric graphs and their disjoint compatible geometric matchings. Given a cycle (a polygon) P we want to draw a set of pairwise disjoint straight-line edges…
The Number of Convex Polyominoes with Given Height and Width
Kevin Buchin, Man-Kwun Chiu, Stefan Felsner +2
We give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that…
The Partition Spanning Forest Problem
Philipp Kindermann, Boris Klemz, Ignaz Rutter +2
Given a set of colored points in the plane, we ask if there exists a crossing-free straight-line drawing of a spanning forest, such that every tree in the forest contains exactly t…
Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles
Philipp Kindermann, Fabrizio Montecchiani, Lena Schlipf +1
We show that the 1-planar slope number of 3-connected cubic 1-planar graphs is at most 4 when edges are drawn as polygonal curves with at most 1 bend each. This bound is obtained b…
On Gallai's conjecture for series-parallel graphs and planar 3-trees
Philipp Kindermann, Lena Schlipf, André Schulz
A path cover is a decomposition of the edges of a graph into edge-disjoint simple paths. Gallai conjectured that every connected -vertex graph has a path cover with at most $\lc…