10 papers
Unit distance graphs with few crossings per edge
Panna Gehér, Dömötör Pálvölgyi, Dániel G. Simon +1
A graph is called a -planar unit distance graph if it can be drawn in the plane such that every edge is a unit line segment and is involved in at most crossings. We investig…
Monochromatic configurations on a circle
Gábor Damásdi, Nóra Frankl, János Pach +1
If we two-colour a circle, we can always find an inscribed triangle with angles whose three vertices have the same colour. In fact, Bialosto…
Stabbing non-piercing sets and face lengths in large girth plane graphs
Dömötör Pálvölgyi, Kristóf Zólomy
We show that a non-piercing family of connected planar sets with bounded independence number can be stabbed with a constant number of points. As a consequence, we answer a question…
A note on infinite versions of -theorems
Attila Jung, Dömötör Pálvölgyi
We prove that fractional Helly and -theorems imply -theorems in an entirely abstract setting. We give a plethora of applications, including reproving almost al…
Piercing intersecting convex sets
Imre Bárány, Travis Dillon, Dömötör Pálvölgyi +1
Assume two finite families and of convex sets in have the property that for every and $B\in \math…
-dimensional transversals for fat convex sets
Attila Jung, Dömötör Pálvölgyi
We prove a fractional Helly theorem for -flats intersecting fat convex sets. A family of sets is said to be -fat if every set in the family contains a ball and…