Alexander Metzger

The Genus of Bipartite Kneser Graphs

We determine the orientable genus of an infinite family of bipartite Kneser graphs. The graph $H(h,2)$ has two copies of the two-element subsets of $[h]$, with opposite-class vertices adjacent when the corresponding subsets are disjoint. For every prime $h>3$ with $h\equiv3\pmod8$, we prove $$ \gamma(H(h,2))=1-\frac{h(...