Abstract:

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 and also
time slot assignments in RFID protocols.

(Note: the speaker does not encourage individuals to color
antennas.)