Dualities and reciprocities on graphs on surfaces

Woo-Seok Jung; Jaeseong Oh

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arXiv · 2005.01590

Dualities and reciprocities on graphs on surfaces

Woo-Seok Jung·Jaeseong Oh

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Abstract

We extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally bi-walkable orientations. In addition, we provide a reciprocity theorem connecting local tensions and boundary acyclic orientations. Furthermore, we define the balanced flow polynomial which is connected with tension polynomial by duality and with totally bi-walkable orientations by reciprocity.

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Woo-Seok Jung, Jaeseong Oh. 2021-09-09. Dualities and reciprocities on graphs on surfaces. https://arxiv.org/abs/2005.01590

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