Current Research





My focus right now is on enumerating perfect matchings of graphs, especially non-bipartite or nonplanar graphs.

Most of the theory in this field has been developed for the bipartite planar case, and especially for nonplanar graphs there are only a handful of existing enumerative results.

I have several partial enumeration results either confirmed or conjectured, including a divisibility result on the number of matchings of the graph in this page's background—maybe the first result of any kind concerning matchings of a three-dimensional crystal lattice!