Holomorphic quadratic differentials on graphs and the chromatic polynomial
Combinatorics
2018-03-02 v1
Abstract
We study "holomorphic quadratic differentials" on graphs. We relate them to the reactive power in an LC circuit, and also to the chromatic polynomial of a graph. Specifically, we show that the chromatic polynomial of a graph , at negative integer values, can be evaluated as the degree of a certain rational mapping, arising from the defining equations for a holomorphic quadratic differential. This allows us to give an explicit integral expression for .
Keywords
Cite
@article{arxiv.1803.00115,
title = {Holomorphic quadratic differentials on graphs and the chromatic polynomial},
author = {Richard Kenyon and Wai Yeung Lam},
journal= {arXiv preprint arXiv:1803.00115},
year = {2018}
}