Author

Austin Ulrigg

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Preprint Oct 2026

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(...

Austin Ulrigg, Alexander Metzger · 0 citations

Preprint Jul 2026

On the Genus Polynomial of Cubic Graphs

The orientable genus polynomial of a graph counts its cellular embeddings by genus. For finite simple $2$-connected cubic graphs it is a cycle-matroid invariant: $M(G)\cong M(H)$ implies $\Gamma_G=\Gamma_H$. The adjacency spectrum and the genus polynomial are incomparable: neither determines the other. We exhibit conne...

Austin Ulrigg · 0 citations