Friday, March 14, 2008 3:30 pm
-
4:30 pm
EDT (GMT -04:00)
Chromatic Zeros of Graphs
| Speaker: | Gordon Royle |
|---|---|
| Affiliation: | University of Western Australia |
| Room: | Mathematics & Computer Building (MC) 5158 |
Abstract:
The
chromatic
polynomial
P(G,k)
of
a
graph
G
is
the
polynomial
that
counts
the
number
of
proper
k-colourings
of
the
graph.
It
was
introduced
in
1912
by
Birkhoff
in
an
attempt
to
find
an
analytic
proof
that
P(G,4)
>
0
whenever
G
is
planar
---
in
other
words,
to
prove
the
4-colour
theorem.
Although
not
successful,
this
work
initiated
the
study
of
the
real
and
complex
zeros
of
the
chromatic
polynomial,
a
subject
that
has
gained
considerable
momentum
over
the
last
few
years,
particularly
due
to
its
interactions
with
statistical
physics.
In
this
talk
I
will
survey
the
current
"state
of
the
art"
in
this
area,
present
some
recent
results
of
my
own
and
discuss
various
open
problems.