C&O PhD student Ahmad Abdi is a recipient of the 2018 Huawei Prize. This award provides $4,000 to a graduate student in the Faculty of Mathematics for demonstration of outstanding achievement in research through a peer-reviewed paper.
Ahmad
was
nominated
for
his
paper
"Packing
odd
T-joins
with
at
most
two
terminals"
(also
available
here),
published
in
the
Journal
of
Graph
Theory
and
co-authored with
his
advisor,
Professor
Bertrand
Guenin.
An
abbreviated
version
of
the
paper
had
appeared
in
the
proceedings
of
the
IPCO
2014
conference.
Ahmad's
paper
proves
an
important
special
case
of
Paul
Seymour's
celebrated
Cycling
Conjecture.
This
conjecture,
first
proposed
in
1977,
is
widely
considered
as
one
of
the
most
challenging
and
fundamental
problems
in
the
area
of
combinatorial
optimization.
The
conjecture
posits
that
binary
Eulerian
matroids
for
which
the
cut
condition
holds
but
which
do
not
have
an
integer
flow
must
contain
one
of
four
possible
obstructions.
This
conjecture
has
far
reaching
consequences,
including
generalizations
of
the
four-colour
theorem
such
as
Tutte's
4-flow
conjecture.
Ahmad's paper proves the Cycling Conjecture for the class of even cycle matroids -- binary matroids that can be obtained as lifts of graphic matroids. The proof uses novel and powerful techniques, as well as tools from matroid theory, graph connectivity, and topological graph theory.