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: ErdosKoRado
theorems, chipfiring and the critical group, KönigEgerváry
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, chipfiring, probabilistic methods), optimization, theoretical
computer science.
Selected publications:
 Uniquely Dcolourable 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.
 KönigEgerváry graphs are nonEdmonds,
Graphs Combin. 26 (2010), 721–726.
 On the stochastic independence properties of hardcore distributions,
Combinatorica 17 (1997), 369391 (with J. Kahn).
Prof. Jenny McNulty, Ph.D.,
University of North Carolina at Chapel Hill, 1993 Research interests:
matroid theory, combinatorics.
Selected publications:
 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).
Prof. George McRae, Ph.D., University
of Washington, 1967
Research interests: homological algebra, ring theory, category theory,
operations research.
Selected publications:
 Toward an elementary axiomatic theory of the category of LPmatroids,
Appl. Categ. Structures 11 (2003), 157–169 (with T.A. AlHawary).
 On Karmarkar's New Projective AlgorithmTheory 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), 187190. (with Hien Nguyen).
Prof. Cory Palmer, Ph.D., Central European University, 2008
Research interests: graph colorings, extremal set systems and applied problems in graph theory.
Selected publications:
 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
H. Liu).
 A new type of edgederived vertex coloring,
Discrete Math. 309 (2009), 63446352 (with E. Gyori).
 The unbalance of set systems,
Graphs Combin. 24 (2008), 361365 (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.

