2 citations · 2 across the 5 of their papers we have counts for
6 papers
On the number of edges of restricted matchstick graphs
Panna Gehér, János Pach, Konrad Swanepoel +1
A graph whose vertices are points in the plane and whose edges are noncrossing straight-line segments of unit length is called a \emph{matchstick graph}. We prove two somewhat coun…
Canonical theorems in geometric Ramsey theory
Panna Gehér, Arsenii Sagdeev, Géza Tóth
In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical…
Diameter reduction via arc reversal
Panna Gehér, Max Kölbl, Lydia Mirabel Mendoza-Cadena +1
The diameter of a directed graph is the maximum distance between any pair of vertices. We study a problem that generalizes \textsc{Oriented Diameter}: For a given directed graph an…
1-planar unit distance graphs
Panna Gehér, Géza Tóth
A matchstick graph is a plane graph with edges drawn as unit distance line segments. This class of graphs was introduced by Harborth who conjectured that a matchstick graph on …
Monochromatic infinite sets in Minkowski planes
Nóra Frankl, Panna Gehér, Arsenii Sagdeev +1
We prove that for any -norm in the plane with and for every infinite , there exists a two-colouring of the plane such that no…
Note on the chromatic number of Minkowski planes: the regular polygon case
Panna Gehér
The famous Hadwiger-Nelson problem asks for the minimum number of colors needed to color the points of the Euclidean plane so that no two points unit distance apart are assigned th…