Strong Hanani-Tutte for the Torus
Radoslav Fulek, Michael J. Pelsmajer, Marcus Schaefer
TL;DR
This paper proves a strong Hanani-Tutte theorem for the torus, showing that certain crossing conditions imply embeddability on the torus, extending planar graph results to a surface of genus one.
Contribution
It establishes a Hanani-Tutte type theorem for the torus, providing a new criterion for graph embeddability on this surface.
Findings
Graphs with even crossings of independent edges can be embedded on the torus.
Extends Hanani-Tutte theorem from planar graphs to toroidal graphs.
Provides a topological characterization for torus embeddings.
Abstract
If a graph can be drawn on the torus so that every two independent edges cross an even number of times, then the graph can be embedded on the torus.
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