### Research

The Department of Mathematics and Applied Mathematical Sciences at URI has a vibrant discrete mathematics group of which I'm privileged to be a part.

My research interests lie principally in structural graph theory, though I am also interested in other areas of combinatorics and discrete mathematics. At the moment I am interested in what structural information can be obtained about a graph from information related to (some combination of) its degree sequence, its induced subgraphs, and its related matrices. I am particularly interested in questions where two or more of these areas overlap.

For a more detailed (but somewhat dated) summary, see my research statement (last updated October 2013). The links below will give you an idea of what I'm currently working on.

#### Recent papers

**Cliques in realization graphs.**Joint work with Nathan Haronian.*Discrete Mathematics*, vol. 346 (January 2023), no. 1, Article 113184. (preprint)**The principal Erdos-Gallai differences of a degree sequence.***Discrete Mathematics*, vol. 345 (April 2022), no. 4, Article 112755. (preprint)**Upward-closed hereditary families in the dominance order.**Joint work with Jean Guillaume.*Discrete Mathematics & Theoretical Computer Science*, vol. 23 (20 January 2022), no. 3. (preprint)-
**Graphs with few trivial characteristic ideals.**Joint work with Carlos A. Alfaro, John Sinkovic, and Ralihe Villagrán.*Linear Algebra and Its Applications*, vol. 615 (15 April 2021), pp. 155-174. (preprint)

For a complete list of my papers and theses, including submitted manuscripts, visit my publications page.

#### Recent talks

- June 14, 2022, SIAM Conference on Discrete Mathematics (DM22), Carnegie Mellon University, Pittsburgh, PA. "Cliques in realization graphs of degree sequences." Slides available by request (PDF, 0.99MB)
- March 25, 2022, Discrete Mathematics Seminar, URI (held virtually). "Cliques in the realization graph of a degree sequence." Slides available by request (PDF, 981KB)
- March 8, 2022, Special Session on Graph Reconfiguration, 53rd Southeastern Conference on Combinatorics, Graph Theory & Computing (Florida Atlantic University, Boca Raton, FL; delivered virtually). "Cliques in the realization graph of a degree sequence." Slides available by request (PDF, 906KB)
- October 15, 2021, Discrete Mathematics Seminar, URI. "The Erdős-Gallai differences of a degree sequence." Slides available by request (PDF, 723KB)
- October 8, 2021, New York Combinatorics Seminar (held virtually), "The Erdős-Gallai differences of a degree sequence." Slides (PDF, 722KB)
- June 5, 2021, MAA Northeastern Section Spring Meeting (held virtually), "Erdős-Gallai differences and complementary degree sequences of graphs." Slides available by request (PDF, 482KB)
- May 27, 2021, CanaDAM 2021 (held virtually) "Unigraphs and hereditary graph classes." Slides available by request (PDF, 937KB)

For a more detailed list, visit my talks and presentations page.

Last updated September 27, 2022.