73 citations · 427 across the 49 of their papers we have counts for
5 papers · 1 filter
Note on the number of edges in families with linear union-complexity
Piotr Micek, Rom Pinchasi
We give a simple argument showing that the number of edges in the intersection graph of a family of sets in the plane with a linear union-complexity is . In parti…
Coloring intersection graphs of arc-connected sets in the plane
Michał Lasoń, Piotr Micek, Arkadiusz Pawlik +1
A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line if the intersection of its any member with is…
Making Octants Colorful and Related Covering Decomposition Problems
Jean Cardinal, Kolja Knauer, Piotr Micek +1
We give new positive results on the long-standing open problem of geometric covering decomposition for homothetic polygons. In particular, we prove that for any positive integer k,…
Coloring Hypergraphs Induced by Dynamic Point Sets and Bottomless Rectangles
Andrei Asinowski, Jean Cardinal, Nathann Cohen +9
We consider a coloring problem on dynamic, one-dimensional point sets: points appearing and disappearing on a line at given times. We wish to color them with k colors so that at an…
Tree-width and dimension
Gwenaël Joret, Piotr Micek, Kevin G. Milans +3
Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural grap…