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09/01/2023
Bichromatic Perfect Matchings with Crossings
We consider bichromatic point sets with n red and n blue points and stud...
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08/21/2023
Different Types of Isomorphisms of Drawings of Complete Multipartite Graphs
Simple drawings are drawings of graphs in which any two edges intersect ...
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03/27/2023
Towards Crossing-Free Hamiltonian Cycles in Simple Drawings of Complete Graphs
It is a longstanding conjecture that every simple drawing of a complete ...
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03/13/2023
Drawings of Complete Multipartite Graphs Up to Triangle Flips
For a drawing of a labeled graph, the rotation of a vertex or crossing i...
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10/21/2022
Blocking Delaunay Triangulations from the Exterior
Given two distinct point sets P and Q in the plane, we say that Q blocks...
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10/02/2022
No Selection Lemma for Empty Triangles
Let S be a set of n points in general position in the plane. The Second ...
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09/02/2022
Shooting Stars in Simple Drawings of K_m,n
Simple drawings are drawings of graphs in which two edges have at most o...
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08/11/2022
Empty Triangles in Generalized Twisted Drawings of K_n
Simple drawings are drawings of graphs in the plane or on the sphere suc...
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05/17/2022
Coloring circle arrangements: New 4-chromatic planar graphs
Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement gr...
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03/11/2022
Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs
Simple drawings are drawings of graphs in which the edges are Jordan arc...
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02/22/2022
Flipping Plane Spanning Paths
Let S be a planar point set in general position, and let 𝒫(S) be the set...
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12/15/2021
Edge Partitions of Complete Geometric Graphs (Part 2)
Recently, the second and third author showed that complete geometric gra...
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09/22/2021
On Crossing-Families in Planar Point Sets
A k-crossing family in a point set S in general position is a set of k s...
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03/17/2021
Adjacency Graphs of Polyhedral Surfaces
We study whether a given graph can be realized as an adjacency graph of ...
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01/11/2021
On Compatible Matchings
A matching is compatible to two or more labeled point sets of size n wit...
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12/14/2020
Crossing-Optimal Extension of Simple Drawings
In extension problems of partial graph drawings one is given an incomple...
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08/20/2020
Plane Spanning Trees in Edge-Colored Simple Drawings of K_n
Károlyi, Pach, and Tóth proved that every 2-edge-colored straight-line d...
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07/20/2020
Rainbow polygons for colored point sets in the plane
Given a colored point set in the plane, a perfect rainbow polygon is a s...
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06/28/2020
Minimizing The Maximum Distance Traveled To Form Patterns With Systems of Mobile Robots
In the pattern formation problem, robots in a system must self-coordinat...
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02/13/2020
Drawing Graphs as Spanners
We study the problem of embedding graphs in the plane as good geometric ...
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09/16/2019
Extending simple drawings with one edge is hard
A simple drawing D(G) of a graph G = (V,E) is a drawing in which two edg...
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08/23/2019
On the edge-vertex ratio of maximal thrackles
A drawing of a graph in the plane is a thrackle if every pair of edges i...
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08/18/2019
Graphs with large total angular resolution
The total angular resolution of a straight-line drawing is the minimum a...
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08/18/2019
On the 2-colored crossing number
Let D be a straight-line drawing of a graph. The rectilinear 2-colored c...
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08/14/2019
Minimal Representations of Order Types by Geometric Graphs
In order to have a compact visualization of the order type of a given po...
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02/16/2019
Flip distances between graph orientations
Flip graphs are a ubiquitous class of graphs, which encode relations ind...
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08/31/2017
Lombardi Drawings of Knots and Links
Knot and link diagrams are projections of one or more 3-dimensional simp...
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08/21/2017