Current Research

I began my graduate work with Professor Dan Archdeacon at UVM, whose specialty is topological graph theory. We did the majority of our work together over lunch at Mansfield House, and have consequently written up a few papers. Some ps and pdf files of papers appear below. (Note: you can open ps files with Ghostview and you can open pdf files with Adobe Acrobat Reader, both free software programs. The ps files are cleaner - some pictures got fuzzy in the conversion to pdf.)

I've also been working on a project with Joanna Ellis-Monaghan at St Michael's College and Dan Archdeacon at UVM on the relationship between biomolecular computing and topological graph theory. Jo has recently written a nice summary of the work, and we are looking forward to submitting a joint paper later in 2006.

I am now a graduate student in the Courant Institute at NYU. I'm working harder studying for qualifying exams than on graph theory! Fortunately, that's a temporary state.

• A Characterization of Projective-Planar Signed Graphs, by D. Archdeacon, M. Debowsky, Discrete Math., 290 (2005), 109-116. [ps file] [pdf file]

• Cycle Systems In The Complete Bipartite Graph Minus A One-Factor, by D. Archdeacon, M. Debowsky, J. Dinitz, H. Gavlas, Discrete Math., 284 (2004), Special Issue In Honor of Curt Lindner On His 65th Birthday, 37-43. [ps file] [pdf file]

• Halin's theorem for the Mobius strip, by D. Archdeacon, C.P. Bonnington, M. Debowsky, M. Prestridge, Ars Combinatoria, 68 (2003) 243-256. [ps file] [pdf file]

• Master's Thesis: Results on Planar Hypergraphs and On Cycle Decompositions, presented April 2002. Advisors: D. Archdeacon and H. Gavlas. [ps file] [pdf file]

• Undergraduate thesis: Graph Theory and Logic, presented December 1999. Advisor: A. Riskin. This contains some very cool pictures generated by a graphics routine that Adrian Riskin wrote for Maple. [MS word file]