Dualities and reciprocities on graphs on surfaces
Combinatorics
2021-09-10 v2
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.
Keywords
Cite
@article{arxiv.2005.01590,
title = {Dualities and reciprocities on graphs on surfaces},
author = {Woo-Seok Jung and Jaeseong Oh},
journal= {arXiv preprint arXiv:2005.01590},
year = {2021}
}
Comments
A revised version, 18 pages, 7 figures