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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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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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06/08/2022
Reconfiguration of Non-crossing Spanning Trees
For a set P of n points in the plane in general position, a non-crossing...
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03/24/2022
Geometric Dominating Sets
We consider a minimizing variant of the well-known No-Three-In-Line Prob...
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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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03/11/2021
Hardness of Token Swapping on Trees
Given a graph where every vertex has exactly one labeled token, how can ...
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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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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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02/13/2020
Drawing Graphs as Spanners
We study the problem of embedding graphs in the plane as good geometric ...
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10/22/2019
Folding Polyominoes with Holes into a Cube
When can a polyomino piece of paper be folded into a unit cube? Prior wo...
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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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07/17/2019
An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
A drawing of a graph in the plane is pseudolinear if the edges of the d...
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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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12/26/2017
Folding Polyominoes into (Poly)Cubes
We study the problem of folding a polyomino P into a polycube Q, allowin...
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08/21/2017
Geodesic Order Types
The geodesic between two points a and b in the interior of a simple poly...
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07/18/2017