The Department of Mathematical Sciences has an active group with interests in discrete mathematics, combinatorial optimization, graph theory, extremal combinatorics, and probabilistic methods. Each year the department offers four or five combinatorics and optimization courses at the junior, senior, and graduate levels. These courses cover the methods, the models, and the theory of combinatorics, graph theory, discrete optimization, and linear programming. In alternate semesters, special topics courses in combinatorics and optimization are offered at the graduate level. Recent topics have included extremal combinatorics, convex polytopes, algebraic combinatorics, and linear optimization. In addition, there is a weekly seminar on combinatorics and optimization-–recent themes have included: Discrete Mathematical Charms of Paul Erdős, chip-firing and the critical group, Erdős-Ko-Rado theorems, König-Egerváry graphs & their relatives, and distinguishing chromatic numbers. The seminar is attended by graduate students and faculty and contributes to an active, engaged C&O community that celebrates its students. Most years, two or three prominent researchers from academia or industry visit our department to give invited lectures and consult.

Faculty

Mark Kayll

Ph.D., Rutgers University, 1994

Research interests: discrete mathematics (e.g. graph coloring, labeling, pebbling, chip-firing, probabilistic methods), theoretical computer science

Selected publications:

• The Erdős-Faber-Lovász Conjecture: Fifty Exciting Years, Mathematics Magazine, to appear.
• Deranged matchings: proofs and conjectures, American Mathematical Monthly 131(2024), 95–111 (with D. Johnston and C. Palmer).
• On colouring oriented graphs of large girth, Contributions to Discrete Mathematics 18(2023), 234–243 (with M. Morris).
• Uniquely D-colourable digraphs with large girth II: simplification via generalization, Electronic Journal of Combinatorics28 (2021), Paper 48, 14pp. (with E. Parsa).
• Integrals don't have anything to do with discrete math, do they?, Mathematics Magazine 84 (2011), 108–119.

Cory Palmer

Ph.D., Central European University, 2008

Research interests: extremal graph theory and combinatorics, applications of graph theory

Selected publications:

• At most 3.55^n stable matchings, in 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science—FOCS 2021, (2022), 217–227 (with D. Pálvölgyi).
• On supersaturation and stability for generalized Turán problems. Journal of Graph Theory 97 (2021), 232–240 (with A. Halfpap).
• Extremal results for Berge hypergraphs, SIAM Journal on Discrete Mathematics 31 (2017), 2314–2327 (with D. Gerbner).
• On the tree packing conjecture, SIAM Journal on Discrete Mathematics 27 (2013), 1995-2006 (with J. Balogh).
• On the Turán number of forests, Electronic Journal of Combinatorics20 (2013), Paper 62, 13 pp. (with B. Lidický and H. Liu).