I received my Ph.D. from The Ohio State University in December 2012. My dissertation “Some topics concerning graphs, signed graphs, and matroids” was supervised by Prof. Neil Robertson. (I was his last (22) Ph.D. student.)
Research Interests: Graph Theory, Signed Graphs, Matroid Theory
Particular topics of interest include well-quasi-ordering, graph invariants (particularly chromatic number, Hadwiger number, girth), minor-closed classes of graphs, induced subgraphs, signed graphs, matroids coming from graphs, signed-graphic matroids, and statistical properties of matroids.
1. Two short proofs of the bounded case of S. B. Rao's degree sequence conjecture, Discrete Math. 313 (2013), no. 13, 1500-1501.
2. Bicircular signed-graphic matroids, Discrete Math. 328 (2014), 1–4.
3. A unified proof of Brooks’ theorem and Catlin’s theorem, Discrete Math. 338 (2015) no. 2, 272–273.
4. (with John Maharry, Neil Robertson, and Daniel Slilaty) Flexibility of projective-planar embeddings, J. Combin. Theory Ser. B 122 (2017), 241–300.
5. (with Richard Behr and Thomas Zaslavsky) Mock threshold graphs, submitted.
6. Some problems on induced subgraphs, submitted.
Current projects include understanding some hereditary classes of graphs, chi-boundedness, antivoltages in graphs, and the ubiquitous Tutte polynomial.
1. Signings of the Heawood graph.
2. On strongly regular graphs.
3. On a problem of Dijkstra.
1. (with Dan Slilaty) Antivoltages in groups of small order.
2. (with Ravindra Bapat, Richard Behr, and Thomas Zaslavsky) Smocks.
Coauthors of papers submitted:
Thomas Zaslavsky https://www2.math.binghamton.edu/p/people/zaslav/start
Richard Behr https://www2.math.binghamton.edu/p/people/grads/behr/start