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On the Maximum Number of Crossings in Star-Simple Drawings of with No Empty Lens
Stefan Felsner, Michael Hoffmann, Kristin Knorr +1
A star-simple drawing of a graph is a drawing in which adjacent edges do not cross. In contrast, there is no restriction on the number of crossings between two independent edges. W…
Simple Topological Drawings of -Planar Graphs
Michael Hoffmann, Chih-Hung Liu, Meghana M. Reddy +1
Every finite graph admits a \emph{simple (topological) drawing}, that is, a drawing where every pair of edges intersects in at most one point. However, in combination with other re…
Plane Spanning Trees in Edge-Colored Simple Drawings of
Oswin Aichholzer, Michael Hoffmann, Johannes Obenaus +5
Károlyi, Pach, and Tóth proved that every 2-edge-colored straight-line drawing of the complete graph contains a monochromatic plane spanning tree. It is open if this statement gene…
Simple -Planar Graphs are Simple -Quasiplanar
Patrizio Angelini, Michael A. Bekos, Franz J. Brandenburg +8
A simple topological graph is -quasiplanar () if it contains no pairwise crossing edges, and -planar if no edge is crossed more than times. In this paper, we…
The Planar Tree Packing Theorem
Markus Geyer, Michael Hoffmann, Michael Kaufmann +2
Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing…
Computing Nonsimple Polygons of Minimum Perimeter
Sándor P. Fekete, Andreas Haas, Michael Hemmer +8
We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertic…