Generalised Kauffman Clock Theorems
Geometric Topology
2025-10-06 v1 Combinatorics
Abstract
Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact oriented surfaces. The proofs use results of Propp providing distributive lattice structures on matchings on bipartite plane graphs, and orientations of graphs with fixed circulation.
Cite
@article{arxiv.2510.02911,
title = {Generalised Kauffman Clock Theorems},
author = {Nguyen Thanh Tung Le and Daniel V. Mathews},
journal= {arXiv preprint arXiv:2510.02911},
year = {2025}
}
Comments
62 pages, 25 figures