**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 in Lippitt 204.
Seminar archive.

Speaker | Niko Townsend, URI |

Title | Lazy Cops and Robbers on Graphs: Chess Graphs and Large Lazy Cop Number |

Time | Friday March 23, 2018, 1-2pm, Lippitt 204 |

Abstract | In the game of Cops and Robbers on Graphs, a team of cops and a robber take turns moving on the vertex set of a graph. If a cop occupies the same vertex as the robber, then the cops win. If it can be shown that the robber can evade the cops indefinitely, then he wins. Primarily, we consider the variant of the game called Lazy Cops and Robbers, wherein only one cop is allowed to move per turn. We give bounds for the cop numbers and lazy cop numbers of Queens Graphs, and examine both games on Rooks Graphs. We also will discuss the properties of the n x n Rooks Graph in depth, as well as share progress toward proving that it is the unique smallest graph with lazy cop number n. |

**News**

- 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,
Associate Dean at the College of Arts and Sciences, graph theory

Barbara Kaskosz, analysis
and its applications to discrete mathematics

William Kinnersley,
graph theory and combinatorial games

Alexandr Kodess, algebraic combinatorics

Lubos Thoma, extremal and probabilistic combinatorics

**Doctoral students**

Jean Guillaume

John Jones

Eric Peterson

**Graduate courses **
MTH547 *Combinatorics*,
MTH548 *Graph Theory*,
MTH515/516 *Algebra*,
MTH550 *Probability and Stochastic Processes*,
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**

- Brown Discrete Mathematics seminar
- MIT Combinatorics seminar
- MIT Probability seminar
- ICERM
- CMSA
- Yale Combinatorics and probability seminar