Combinatorics and Optimization
The Department of Mathematical Sciences has an active group
with interests in discrete mathematics, matroid theory,
combinatorial optimization, graph theory, extremal
combinatorics, and probabilistic methods. Each year the
department offers five or six combinatorics and optimization
courses at the junior, senior, and graduate levels. These
courses cover the methods, the models, and the theory of
discrete optimization, linear programming, and graph theory. In
alternate semesters, special topics courses in combinatorics and
optimization are offered at the graduate level. Recent topics
have included extremal combinatorics, convex polytopes, matroid
theory, algebraic combinatorics, and linear optimization. In
addition there is a weekly seminar on combinatorics and
optimization - recent themes have included: Erdos-Ko-Rado
theorems, chip-firing and the critical group, König-Egerváry
graphs and their relatives, and distinguishing chromatic
numbers. Most years, two or three prominent researchers from
academia or industry visit our department to give invited
lectures and consult.
Combinatorics and Optimization Faculty
Prof. Mark Kayll,
Ph.D., Rutgers University, 1994
Research interests: discrete mathematics (e.g. graph coloring, labeling,
pebbling, chip-firing, probabilistic methods), optimization, theoretical
- Uniquely D-colourable digraphs with large girth,
Canad. J. Math. 64 (2012), 1310–1328 (with A. Harutyunyan,
B. Mohar, and L. Rafferty).
- Integrals don't have anything to do with discrete math, do they?,
Math. Mag. 84 (2011), 108–119.
- König-Egerváry graphs are non-Edmonds,
Graphs Combin. 26 (2010), 721–726.
- On the stochastic independence properties of hard-core distributions,
Combinatorica 17 (1997), 369-391 (with J. Kahn).
Prof. Jenny McNulty, Ph.D.,
University of North Carolina at Chapel Hill, 1993 Research interests:
matroid theory, combinatorics.
Prof. George McRae, Ph.D., University
of Washington, 1967
- Matroids: a geometric introduction,
Cambridge University Press, Cambridge, 2012 (with G. Gordon).
- Magic squares and antimagic graphs, Bulletin of the ICS
58 (2010) 83–93. (with P.M. Kayll, J. Mihalisin)
- On cocircuit covers of bicircular matroids,
Discrete Math. 308 (2008), 4008–4013, (with N.A. Neudauer).
Research interests: homological algebra, ring theory, category theory,
Prof. Cory Palmer, Ph.D., Central European University, 2008
- Toward an elementary axiomatic theory of the category of LP-matroids,
Appl. Categ. Structures 11 (2003), 157–169 (with T.A. Al-Hawary).
- On Karmarkar's New Projective Algorithm-Theory and Applications
(invited address), Decision Sciences Institute (Phoenix 1986).
- A Network Model for Determining Trunk Lines with Redundancy,
Ninth Annual Proceedings of American Institute for Decision
Sciences, (1980), 187-190. (with Hien Nguyen).
Research interests: graph colorings, extremal set systems and applied problems in graph theory.
- On the tree packing conjecture,
SIAM J. Discrete Math. 27 (2013), 1995–2006 (with J. Balogh).
- On the Turán number of forests,
Electron. J. Combin. 20 (2013), Paper 62, 13 pp. (with B. Lidický and
- A new type of edge-derived vertex coloring,
Discrete Math. 309 (2009), 6344-6352 (with E. Gyori).
- The unbalance of set systems,
Graphs Combin. 24 (2008), 361-365 (with N. Lemons).
Other faculty members with interests and backgrounds in probability,
statistics, algebra, analysis, computing and mathematical modeling
often interact with and participate in the combinatorics and optimization
activities of the department.