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What induces plane structures in complete graph drawings?
Alexandra Weinberger, Ji Zeng
This paper considers the task of connecting points on a piece of paper by drawing a curve between each pair of them. Under mild assumptions, we prove that many pairwise disjoint cu…
Grounded String Representations of Series-Parallel Graphs without Transitive Edges
Sabine Cornelsen, Jan Kratochvíl, Miriam Münch +3
In a {\em grounded string representation} of a graph there is a horizontal line and each vertex is represented as a simple curve below with one end point on su…
Characterizing and Recognizing Twistedness
Oswin Aichholzer, Alfredo García, Javier Tejel +2
In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills…
Different Types of Isomorphisms of Drawings of Complete Multipartite Graphs
Oswin Aichholzer, Birgit Vogtenhuber, Alexandra Weinberger
Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze s…
Drawings of Complete Multipartite Graphs Up to Triangle Flips
Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang +5
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended r…
Shooting Stars in Simple Drawings of
Oswin Aichholzer, Alfredo García, Irene Parada +2
Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every…
Empty Triangles in Generalized Twisted Drawings of
Alfredo García, Javier Tejel, Birgit Vogtenhuber +1
Simple drawings are drawings of graphs in the plane or on the sphere such that vertices are distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect a…
Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs
Oswin Aichholzer, Alfredo García, Javier Tejel +2
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a sp…
Removing Popular Faces in Curve Arrangements
Phoebe de Nooijer, Soeren Terziadis, Alexandra Weinberger +4
A face in a curve arrangement is called popular if it is bounded by the same curve multiple times. Motivated by the automatic generation of curved nonogram puzzles, we investigate…
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…