We prove Pisanski's conjecture on quadrilateral embeddings of regular bipartite graphs. For integers m ≥ d ≥ 4 with 4 | md, we construct both a connected simple d-regular bipartite graph G with m vertices in each bipartition class and an orientable quadrangulation.
Submitted to Journal of Graph TheoryResearch
My research interests are in topological graph theory, especially graph embeddings, orientable genus, rotation systems, and forbidden minors.
Alexander Metzger and I construct a vertex-transitive orientable quadrangulation of the bipartite Kneser graph H(h,2) for every prime h > 3 with h ≡ 3 (mod 8). It attains the Euler lower bound and therefore determines the genus.
Submitted to Journal of Graph TheoryAlexander Metzger and I wrote PAGE, an algorithm that computes the orientable genus of a connected graph by searching over its rotation systems. We used it to show that the (3,12)-cage has genus 17, and it is now in SageMath and used by the House of Graphs to compute graph genus.
My undergraduate honors thesis, advised by François Clément, on embedding graphs on surfaces. The later sections cover PAGE and the forbidden toroidal minors.