Forests, trees, and matchings can always be reconfigured on the torus and higher-genus orientable surfaces by rerouting one edge at a time while maintaining crossing-free embeddings.
Proc.\ 32nd ACM-SIAM Symposium on Discrete Algorithms (
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Rerouting Curves on Surfaces
Forests, trees, and matchings can always be reconfigured on the torus and higher-genus orientable surfaces by rerouting one edge at a time while maintaining crossing-free embeddings.