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Move-reduced graphs on a torus

Published Web Location

https://doi.org/10.1090/tran/9168Creative Commons 'BY' version 4.0 license
Abstract

We determine which bipartite graphs embedded in a torus are move-reduced. In addition, we classify equivalence classes of such move-reduced graphs under square/spider moves. This extends the class of minimal graphs on a torus studied by Goncharov–Kenyon, and gives a toric analog of Postnikov’s and Thurston’s results on a disk.

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