19 citations · 21 across the 23 of their papers we have counts for
11 papers · 1 filter
On the Uncrossed Number of Graphs
Martin Balko, Petr Hliněný, Tomáš Masařík +3
Visualizing a graph in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masařík and Hliněný [GD 2023] recently a…
Towards Crossing-Free Hamiltonian Cycles in Simple Drawings of Complete Graphs
Oswin Aichholzer, Joachim Orthaber, Birgit Vogtenhuber
It is a longstanding conjecture that every simple drawing of a complete graph on vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to "t…
Compatible Spanning Trees in Simple Drawings of
Oswin Aichholzer, Kristin Knorr, Wolfgang Mulzer +6
For a simple drawing of the complete graph , two (plane) subdrawings are compatible if their union is plane. Let be the set of all plane spanning trees on…
Coloring circle arrangements: New -chromatic planar graphs
Man-Kwun Chiu, Stefan Felsner, Manfred Scheucher +3
Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement graphs of simple great-circle arrangements have chromatic number at most . Motivated by this conjecture, we…
Edge Partitions of Complete Geometric Graphs (Part 2)
Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber +5
Recently, the second and third author showed that complete geometric graphs on vertices in general cannot be partitioned into plane spanning trees. Building up on this wor…
On weighted sums of numbers of convex polygons in point sets
Clemens Huemer, Deborah Oliveros, Pablo Pérez-Lantero +2
Let be a set of points in general position in the plane, and let be the number of convex -gons with vertices in that have exactly points of $S…