Alan
Arroyo,
Combinatorics
&
Optimization,
University
of
Waterloo
"Jordan
Curve
Theorem:
a
proof
using
graphs."
Jordan
Curve
Theorem
states
that
every
non-self-intersecting
closed
curve
divides
the
plane
into
two
regions.
Although
this
theorem
seems
obvious,
Bolzano
was
the
first
to
point
out
that
proving
this
fact
is
not
easy.
The
first
proof
is
historically
attributed
to
Camille
Jordan
in
1887,
and
in
the
last
century
many
other
proofs
have
been
discovered.
Some
of
the
most
recent
ones
are
short
and
elementary.
For
instance,
the
one
given
by
Carsten
Thomassen
in
1992
uses
only
elementary
results
from
Graph
Theory.
In
this
talk
I
will
sketch
this
proof,
and
mention
some
of
the
difficulties
that
make
this
theorem
not
so
obvious.
MC 5479