Shortest Paths, Convexity, and Treewidth in Regular Hyperbolic Tilings

Sándor Kisfaludi-Bak, Tze-Yang Poon, Geert van Wordragen

Hyperbolic tilings are natural infinite planar graphs where each vertex has degree $q$ and each face has $p$ edges for some $\frac{1}{p}+\frac{1}{q}<\frac{1}{2}$. We study the structure of sho…