Determining Genus From Sandpile Torsor Algorithms

Alex McDonough

Determining Genus From Sandpile Torsor Algorithms

Alex McDonough

Abstract

We provide a pair of ribbon graphs that have the same rotor routing and Bernardi sandpile torsors, but different topological genus. This resolves a question posed by M. Chan [Cha]. We also show that if we are given a graph, but not its ribbon structure, along with the rotor routing sandpile torsors, we are able to determine the ribbon graph's genus. Comment: Reformatted for DMTCS

Keywords

• Mathematics - Combinatorics

Mathematics Subject Classification 2020

• 05C10 - Planar graphs; geometric and topological aspects of graph theory
• 05C85 - Graph algorithms (graph-theoretic aspects)

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