My research interests lie principally in structural and extremal 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 its degree sequence and/or the subgraphs it does or does not induce. I am particularly interested where the two areas overlap--in graph problems seeking to relate the presence or absence of induced subgraphs in a graph G to conditions on the degree sequence of G.
For a more detailed (but slightly 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.
- Adjacency relationships forced by a degree sequence. To appear in Graphs and Combinatorics. (preprint)
- On 1-uniqueness and dense critical graphs for tree-depth. Joint work with John Sinkovic. Discrete Mathematics, vol. 341 (2018), no. 7, pp. 1973-1982. (preprint)
- Weakly threshold graphs. Discrete Mathematics & Theoretical Computer Science, vol. 20 (2018), no. 1, paper 15.
- Neighborhood degree lists of graphs. Joint work with Elizabeth Donovan. Discrete Mathematics, vol. 341 (2018), no. 1, pp. 175-183. (preprint)
- Colored saturation parameters for rainbow subgraphs. Joint work with Michael Ferrara, Jennifer Vandenbussche, and Paul S. Wenger. Journal of Graph Theory, vol. 86 (2017), no. 4, pp. 375-386. (preprint)
For a complete list of my papers and theses, visit my publications page.
- January 6, 2018, 2018 International Workshop on Graph Theory, Ewha Womans University, Seoul, Korea. "Looking upward in the dominance order." Slides available by request (PDF, 752KB)
- November 3, 2017, Discrete Mathematics Seminar, URI. "Independence number and the Havel-Hakimi residue." Slides (PDF, 472KB)
- June 3, 2017, MAA Northeastern Section Spring Meeting (Norwich University, Northfield, VT). "Uniqueness in tree-depth labelings of graphs." Slides (PDF, 301KB)
- April 5, 2017, VCU Discrete Mathematics Seminar (Virginia Commonwealth University, Richmond, VA). "Erdos-Gallai near-equalities and the graphs that exhibit them." Slides (PDF, 1269KB)
- March 24, 2017, Discrete Mathematics Seminar, URI. "The Grone-Merris Conjecture."
- March 8, 2017, 48th Southeastern International Conference on Combinatorics, Graph Theory & Computing (Florida Atlantic University, Boca Raton, FL). "Graphs with low Erdos-Gallai differences." Slides (PDF, 672KB)
- January 6, 2017, Joint Mathematics Meetings (Atlanta, GA). "Uniqueness in labelings of tree-depth-critical graphs." Slides (PDF, 289KB)
For a more detailed list, visit my talks and presentations page.
Partially updated June 15, 2018.