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.
- Weakly threshold graphs. Submitted.
- Adjacency relationships forced by a degree sequence. Submitted.
- On 1-uniqueness and dense critical graphs for tree-depth. Joint work with John Sinkovic. Submitted.
- Neighborhood degree lists of graphs. Joint work with Elizabeth Donovan. To appear in Discrete Mathematics.
- Colored saturation parameters for rainbow subgraphs. Joint work with Michael Ferrara, Jennifer Vandenbussche, and Paul S. Wenger. Published online 8 March 2017 in Journal of Graph Theory. DOI: 10.1002/jgt.22132. (preprint)
- On realization graphs of degree sequences. Discrete Mathematics, vol. 339 (2016), no. 8, pp. 2146-2152. (preprint)
- Graphs with the strong Havel-Hakimi property. Joint work with Grant Molnar. Graphs and Combinatorics, vol. 32 (2016), pp. 1689-1697. (preprint)
- Uniqueness and minimal obstructions for tree-depth. Joint work with John Sinkovic. Discrete Mathematics, vol. 339 (2016), no. 2, 606-613. (preprint)
For a complete list of my papers and theses, visit my publications page.
- 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)
- November 19, 2016, MAA Northeastern Section Fall Meeting (Trinity College, Hartford, CT). "A Strong Havel-Hakimi Property for Graphs."
For a more detailed list, visit my talks and presentations page.
Last updated November 9, 2017.