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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...

0 Oswin Aichholzer, et al. ∙

∙ 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 ...

0 Oswin Aichholzer, et al. ∙

∙ 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 ...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 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 ...

0 Ruy Fabila-Monroy, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 Alfredo Garcia, et al. ∙

∙ 05/17/2022

Coloring circle arrangements: New 4-chromatic planar graphs

Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement gr...

0 Man-Kwun Chiu, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 02/22/2022

Flipping Plane Spanning Paths

Let S be a planar point set in general position, and let 𝒫(S) be the set...

0 Oswin Aichholzer, et al. ∙

∙ 12/15/2021

Edge Partitions of Complete Geometric Graphs (Part 2)

Recently, the second and third author showed that complete geometric gra...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 03/17/2021

Adjacency Graphs of Polyhedral Surfaces

We study whether a given graph can be realized as an adjacency graph of ...

0 Elena Arseneva, et al. ∙

∙ 01/11/2021

On Compatible Matchings

A matching is compatible to two or more labeled point sets of size n wit...

0 Oswin Aichholzer, et al. ∙

∙ 12/14/2020

Crossing-Optimal Extension of Simple Drawings

In extension problems of partial graph drawings one is given an incomple...

0 Robert Ganian, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 David Flores-Peñaloza, et al. ∙

∙ 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...

0 Jared Coleman, et al. ∙

∙ 02/13/2020

Drawing Graphs as Spanners

We study the problem of embedding graphs in the plane as good geometric ...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 Alan Arroyo, et al. ∙

∙ 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...

0 Oswin Aicholzer, et al. ∙

∙ 08/18/2019

Graphs with large total angular resolution

The total angular resolution of a straight-line drawing is the minimum a...

0 Oswin Aichholzer, et al. ∙

∙ 08/18/2019

On the 2-colored crossing number

Let D be a straight-line drawing of a graph. The rectilinear 2-colored c...

0 Oswin Aichholzer, et al. ∙

∙ 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...

0 Oswin Aichholzer, et al. ∙

∙ 02/16/2019

Flip distances between graph orientations

Flip graphs are a ubiquitous class of graphs, which encode relations ind...

0 Oswin Aichholzer, et al. ∙

∙ 08/31/2017

Lombardi Drawings of Knots and Links

Knot and link diagrams are projections of one or more 3-dimensional simp...

0 Philipp Kindermann, et al. ∙

∙ 08/21/2017

Geodesic Order Types

The geodesic between two points a and b in the interior of a simple poly...

0 Oswin Aichholzer, et al. ∙

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