Friday, January 30, 2009 3:30 pm
-
4:30 pm
EST (GMT -05:00)
Recent results on planarity
| Speaker: | Bruce Richter |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics & Computer Building (MC) 5158 |
Abstract:
Three
well-known
characterizations
of
planarity
of
graphs
are
the
theorems
of
Kuratowski,
MacLane,
and
Whitney.
The
first
is
about
forbidden
subgraphs,
the
second
about
a
basis
for
the
cycle
space,
and
the
third
is
about
dual
graphs.
Thomassen
generalized
Kuratowski's
Theorem
to
"2-connected,
compact,
locally
connected
metric
spaces",
Bruhn
and
Stein
proved
MacLane's
Theorem
for
the
Freudenthal
compactification
of
a
locally
finite
graph.
Bruhn
and
Diestel
proved
a
version
of
Whitney's
Theorem
for
(compactifications
of
certain)
infinite
graphs.
In
this
talk,
we
will
see
how
to
omit
the
"2-connected"
hypothesis
from
Thomassen's
Theorem
and
generalize
both
of
the
other
two
theorems
to
compact
graph-like
spaces.