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Felix Lazebnik is an internationally recognized expert in the field of graph theory.
For those who hear the phrase “graph theory” and think of the basic
pie charts and bar graphs introduced in elementary school, there’s a new
world to be explored.
“In graph theory, the most simple way to think of a graph is as a set
of points joined by segments,” said Felix Lazebnik, professor of
mathematical sciences at the University of Delaware and an
internationally known expert in graph theory. “Graph theory has become
the common language for discrete mathematics … especially with the
advent of computer science.”
Lazebnik is one of three researchers working in graph theory whose
work was celebrated at a conference at UD in early August. Tthe Algebraic and Extremal Graph Theory Conference was attended by more
than 80 mathematicians from around the world and featured 14 invited
speakers from the U.S., Canada, the Netherlands, Spain, China, Israel
In addition to Lazebnik, the conference honored the work of Willem
Haemers of Tilburg University in the Netherlands and Andrew Woldar of
Villanova University. All three delivered talks at the event.
Graphs—the dot-and-line kind that are highly useful in such diverse
fields as computer science, linguistics, chemistry and sociology—can be
seen as similar to a network, where the problem lies in connecting the
dots by drawing lines in particular ways.
Lazebnik described a very simple example in interpersonal relations: A
group of seven people can be represented by drawing seven points, or
dots, on a flat piece of paper. Lines can then be drawn between any
pairs of individuals who know each other. When the drawing is finished,
it can serve as a visual answer to various questions, such as which
person has the most acquaintances or how many individuals know only one
other person in the group.
Much larger and more complex graphs can be created as models for
everything from how various areas of the brain are connected to how
diseases spread through populations. In another example, the methods
used by search engines to rank web pages come from recent techniques in
“Graph theory studies all these possible applications,” Lazebnik
said. “When you have a question, you can translate it into the language
That translation requires relying on theory, said Eric Moorhouse,
professor of mathematics at the University of Wyoming, who often draws
simple graphs to use in his teaching. But in real situations,
particularly in computer science, “Most of the graphs we are concerned
with are much too complicated to be meaningfully represented by drawings
or physical models,” he said.
Move this whole section up, swapping places with the section above it.
This simple graph, known as a Heawood graph, has 14 vertices or
points (represented by screws) and 21 edges or segments (represented by
strings). Each screw is joined to exactly three others, and the shortest
path you can find that follows a string and brings you back to the same
screw where you started requires six segments of string. The Heawood
graph is the smallest graph with these properties, which means it can be
called “extremal.” One of the subjects of the recent conference at UD was
Lazebnik “is one of the most important researchers in graph theory,”
whose work in 1995 on constructing a particular kind of graph “is still
the best in the world,” said Sebastian Cioabă, associate professor of
mathematical sciences at UD and one of the conference organizers.
Lazebnik, who was born and grew up in Kiev, Ukraine, in what was then
the Soviet Union, earned his master’s degree in mathematics at Kiev
State University. He taught high school for four years at a boarding
school at the university, where students from throughout Ukraine were
able to study more advanced math and physics than were offered at other
Even today, Lazebnik said, that high school teaching experience, in
which he worked with the same youngsters for three years and so got to
know them well and help them develop their skills over time, remains one
of his most meaningful and enjoyable jobs. He is still in touch with
many of his former students, some of whom have gone on to their own
careers in mathematics.
“On the other hand, I would never have been able to study mathematics
further and do active research if I continued that work,” he said, so
when the opportunity to leave the Soviet Union arose, he and his family
came to the United States.
Arriving in Philadelphia with little knowledge of the American system
of higher education, he wrote letters to several mathematicians, who
offered him “remarkable advice and support,” he said. The first thing he
learned was that, in order to teach at a university, he would need a
Lazebnik applied to the University of Pennsylvania, without even
knowing the school’s reputation and Ivy League status, and was accepted.
He worked part-time as a lecturer and teaching assistant—and, during a
yearlong leave of absence from Penn, as a full-time actuarial assistant
at an insurance company—and earned his doctorate in 1987. He joined the
UD faculty that same year.
He is the author of numerous papers in academic journals and serves
on the editorial board of the Electronic Journal of Combinatorics. He
has supervised many undergraduate and graduate students, and is
currently working with three doctoral students.
The conference seeks to “expand, deepen and broaden the research” in
new areas of graph theory, according to the National Science Foundation,
one of the sponsors. Other sponsors are UD’s Department of Mathematical
Sciences, Villanova University, Muhlenberg College, the Center for
Discrete Mathematics and Theoretical Computer Science at Rutgers
University, the International Linear Algebra Society and the Institute
for Mathematics and Its Applications.
Article by Ann Manser; illustrations by Jeff Chase and courtesy of Eric Moorhouse