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 204. Seminar archive.

Speaker Lilith Wagstrom, URI

Title The tree-depth and criticality of unicyclic graphs

Time Friday March 28, 2025, 1pm, Lippitt 204

Abstract The tree-depth of a graph G is defined as the smallest k for which there exists a proper labeling L of G such that if L(x) = L(y) then every path between x and y must contain a vertex z with L(z) > L(x). The graph G is k-critical if it has tree-depth k and every proper minor of G has tree-depth at most k-1. We investigate when unicyclic graphs are critical. Despite unicyclic graphs' relatively simple structure it is surprisingly difficult to classify when they are critical. Part of this difficulty arises from the large variance of structures in unicyclic graphs. We present several families of critical unicyclic graphs that vary greatly in structure. However, despite the difficulty we will go over a potential classification of critical unicyclic graphs. In addition to these results, we present patterns present in the optimal feasible tree-depth labelings of cycles and general graphs.

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	Lilith Wagstrom, URI
Title	The tree-depth and criticality of unicyclic graphs
Time	Friday March 28, 2025, 1pm, Lippitt 204


Abstract	The tree-depth of a graph G is defined as the smallest k for which there exists a proper labeling L of G such that if L(x) = L(y) then every path between x and y must contain a vertex z with L(z) > L(x). The graph G is k-critical if it has tree-depth k and every proper minor of G has tree-depth at most k-1. We investigate when unicyclic graphs are critical. Despite unicyclic graphs' relatively simple structure it is surprisingly difficult to classify when they are critical. Part of this difficulty arises from the large variance of structures in unicyclic graphs. We present several families of critical unicyclic graphs that vary greatly in structure. However, despite the difficulty we will go over a potential classification of critical unicyclic graphs. In addition to these results, we present patterns present in the optimal feasible tree-depth labelings of cycles and general graphs.

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