Author

Alexander Metzger

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Preprint Oct 2026

Resolving Pisanski's Conjecture

We prove Pisanski's conjecture on quadrilateral embeddings of regular bipartite graphs. For integers $m\geq d\geq4$ with $4\mid md$, we construct both a connected simple $d$-regular bipartite graph $G$ with $m$ vertices in each bipartition class and an orientable quadrangulation. This graph's genus is \[ \ga(G)=1+\frac...

Austin Ulrigg, Alexander Metzger · 0 citations

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 · 1 citation