**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 205**.
Seminar archive.

Speaker | Mathias Schacht, Yale University and Universitaet Hamburg |

Title | Homomorphism threshold for graphs |

Time | Friday November 9, 2018, 1-2pm, Lippitt 205 |

Abstract |
The interplay of minimum degree and 'structural properties' of large
graphs with a given forbidden subgraph is a central topic in extremal
graph theory. For a given graph $F$ we define the homomorphism threshold
as the infimum $\alpha$ such that every $n$-vertex $F$-free graph $G$
with minimum degree $>\alpha n$ has a homomorphic image $H$ of bounded
size (independent of $n$), which is $F$-free as well. Without the
restriction of $H$ being $F$-free we recover the definition of the
chromatic threshold, which was determined for every graph $F$ by Allen
et al. The homomorphism threshold is less understood and we present
recent joint work with O. Ebsen on the homomorphism threshold for odd
cycles. Host: Jie Han |

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

Jie Han, extremal and probabilistic combinatorics

Barbara Kaskosz, analysis
and its applications to discrete mathematics

William Kinnersley,
graph theory and combinatorial games

Lubos Thoma, extremal and probabilistic combinatorics

**Doctoral students**

Jean Guillaume

John Jones

Benjamin Lantz

Eric Peterson

Nikolas Townsend

**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**

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