Colloquium

4:00 p.m., Monday (February 27, 2006)

MATH 105

## Shakhar Smorodinsky Courant Institute of Mathematical Sciences

### Coloring Geometric Hypergraphs

Given a hypergraph H=(V,E), its conflict-free chromatic number (CF-chromatic number) is the minimum number of colors needed to color the vertex set V such that, for every hyperedge S, there is at least one element v \in S whose color is unique (in S).

Note that the CF-chromatic number of a hypergraph H is at least its chromatic number (where each hyperedge of size at least two is required to be non-monochromatic), and at most the colorful chromatic number (where each hyperedge is required to be colorful).

I will survey some recent results on the conflict-free chromatic number of hypergraphs that arise from certain geometric instances and also present open problems for further research. This new" coloring problem is related to the problem of frequency assignment to cellular antennas.

Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge).