# Conflict-Free Coloring of Intersection Graphs of Geometric Objects

### Wednesday, June 14th, 2017 16:10

### Schreiber 309

### Conflict-Free Coloring of Intersection Graphs of Geometric Objects

### Chaya Keller, BGU

### Abstract:

Conflict-Free (CF) coloring is a well studied notion in combinatorics and computational geometry.

One of the motivations to study CF-colorings stems from frequency allocation in wireless networks.

A CF- coloring of a graph is a coloring of its vertices such that the neighborhood

of each vertex contains a vertex whose color differs from the colors of all

other vertices in that neighborhood. Bounds on the CF chromatic number of general graphs were obtained by Pach and Tardos (2009).

In this talk we discuss CF colorings of intersection graphs of geometric objects. We show that any

intersection graph of n pseudo-discs in the plane admits a CF coloring with O(log n) colors. The bound is asymptotically

sharp. Using our methods, we also obtain a strengthening of two theorems of Even et al. (FOCS 2002) on

CF coloring of geometric hypergraphs.

Joint work with Shakhar Smorodinsky.