Discrete Mathematics Group at URI

Discrete Mathematics Group at URI

The faculty of our group is interested in a wide range of areas in discrete mathematics both pure and applied: graph theory, network theory, extremal and probabilistic methods, analytic methods, finite model theory, combinatorial games, combinatorial optimization, bioinformatics applications.

Seminar Our seminar is held Fridays 1-2pm, Lippitt 205. Seminar archive.

Speaker Faith Bailey, URI

Title Choice Numbers of Graphs: a Probabilistic Approach

Time Wednesday February 12, 2025, 1pm, Lippitt 204

Abstract In this seminar we explore key results from the paper Choice Numbers of Graphs: a Probabilistic Approach by Noga Alon. In particular, we will prove there exists a constant $c$, such that the choice number of $K_{m\star r}$ has an upper bound of $s_0=cr\log(m)$. We start with Case 1 where the number of partitions is less than or equal to the number of vertices in each partition, $r\leq m$. Then we will consider Case 2: where the number of partitions is greater than the number of vertices in each partition, $r>m$. This approach gives insights into the probabilistic methods used in the proof and demonstrates how ideas of graph colorings have developed.

News

Discrete Math Day at the University of Rhode Island, September 29, 2018.
Conference announcements at Theorynet, DMANet, and a few other.
Workshop "Non-Combinatorial Combinatorics" will be held at the University of Warwick, 14-16 September 2015, conference webpage.
The 1st Cargese Fall School on Random Graphs will be held in Cargese, Corsica. September 20-25, 2015. Further details can be found at http://math.unice.fr/~dmitsche/Fallschool/Fallschool.html.

Faculty and their research
     Michael Barrus, graph theory
     Nancy Eaton, graph theory
     Barbara Kaskosz, analysis and its applications to discrete mathematics
     William Kinnersley, graph theory and combinatorial games
     Pengyu (Peter) Liu, graph theory and topological combinatorics
     Lubos Thoma, extremal and probabilistic combinatorics

Doctoral students
Lilith Wagstrom
John Jones

Graduate courses MTH547 Combinatorics, MTH548 Graph Theory, MTH515/516 Algebra, MTH550 Probability and Stochastic Processes, MTH581 Optimization Methods, MTH656 Probability on Discrete Structures, CSC541 Advanced Topics in Algorithms, CSC542 Mathematical Analysis of Algorithms, CSC544 Theory of Computation, Special topics courses in Extremal Graph Theory, Ramsey Theory, Algebraic Combinatorics.

Discrete mathematics nearby

MIT Combinatorics seminar Brown Combinatorics seminar / applied seminars

MIT Probability seminar Yale Combinatorics and probability seminar

ICERM CMSA

Speaker	Faith Bailey, URI
Title	Choice Numbers of Graphs: a Probabilistic Approach
Time	Wednesday February 12, 2025, 1pm, Lippitt 204


Abstract	In this seminar we explore key results from the paper Choice Numbers of Graphs: a Probabilistic Approach by Noga Alon. In particular, we will prove there exists a constant $c$, such that the choice number of $K_{m\star r}$ has an upper bound of $s_0=cr\log(m)$. We start with Case 1 where the number of partitions is less than or equal to the number of vertices in each partition, $r\leq m$. Then we will consider Case 2: where the number of partitions is greater than the number of vertices in each partition, $r>m$. This approach gives insights into the probabilistic methods used in the proof and demonstrates how ideas of graph colorings have developed.

MIT Combinatorics seminar		Brown Combinatorics seminar / applied seminars
MIT Probability seminar		Yale Combinatorics and probability seminar
ICERM		CMSA