C&O
PhD
student
James
Davies
is
a
recipient
of
the
Faculty
of
Mathematics
Graduate
Research
Excellence
Award.
James
was
nominated
for
his
paper
Vertex-minor-closed
classes
are
chi-bounded
which
has
been
accepted
for
publication
in
Combinatorica.
The
main
result
of
the
paper
solves
a
conjecture
of
Professor
Jim
Geelen
from
2009,
that
every
class
of
graphs
that
is
closed
under
taking
vertex-minors
is
chi-bounded.
Geelen's
conjecture
was
motivated
by
a
deeper
suspicion
that
vertex-minor-closed
classes
of
graphs
are
highly
structured,
and
he
expected
that
one
would
need
to
uncover
that
structure
in
order
to
prove
the
result.
However,
Davies
was
able
to
prove
the
result
in
full
generality.
His
approach
relied
on
techniques
of
Chudnovsky,
Scott
and
Seymour
on
induced
subgraphs.
Geelen
remarked
that
"the
proof
itself
is
a
tour
de
force
in
combinatorial
reasoning"
and
that
Davies'
theorem
"is
a
truly
outstanding
result".
The
Faculty
of
Mathematics
Graduate
Research
Excellence
Award
is
designed
to
recognize
and
celebrate
research
excellence.
Two
awards
valued
at
$5,000
each
will
be
provided
annually
to
graduate
students
who
are
registered
full
time
in
the
Faculty
of
Mathematics.
