73 citations · 427 across the 49 of their papers we have counts for
6 papers · 1 filter
Making Triangles Colorful
Jean Cardinal, Kolja Knauer, Piotr Micek +1
We prove that for any point set P in the plane, a triangle T, and a positive integer k, there exists a coloring of P with k colors such that any homothetic copy of T containing at…
Triangle-free geometric intersection graphs with large chromatic number
Arkadiusz Pawlik, Jakub Kozik, Tomasz Krawczyk +4
Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number. However, until very recently, no su…
Triangle-free intersection graphs of line segments with large chromatic number
Arkadiusz Pawlik, Jakub Kozik, Tomasz Krawczyk +4
In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is n…
Nonrepetitive choice number of trees
Jakub Kozik, Piotr Micek
A nonrepetitive coloring of a path is a coloring of its vertices such that the sequence of colors along the path does not contain two identical, consecutive blocks. The remarkable…
Outerplanar graph drawings with few slopes
Kolja Knauer, Piotr Micek, Bartosz Walczak
We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel…
An extremal problem on crossing vectors
Michał Lasoń, Piotr Micek, Noah Streib +2
For positive integers and , two vectors and from are called -crossing if there are two coordinates and such that and $B[j…