3 papers
math.CO2025
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…
math.CO2024
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…
cs.CG2023
Two trees are better than one
Adrian Dumitrescu, János Pach, Géza Tóth
We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If denotes the length of a mini…