Linear bound in terms of maxmaxflow for the chromatic roots of series-parallel graphs
Combinatorics
2020-01-17 v1
Abstract
We prove that the (real or complex) chromatic roots of a series-parallel graph with maxmaxflow Lambda lie in the disc |q-1| < (Lambda-1)/log 2. More generally, the same bound holds for the (real or complex) roots of the multivariate Tutte polynomial when the edge weights lie in the "real antiferromagnetic regime" -1 \le v_e \le 0. This result is within a factor 1/log 2 \approx 1.442695 of being sharp
Keywords
Cite
@article{arxiv.1307.1721,
title = {Linear bound in terms of maxmaxflow for the chromatic roots of series-parallel graphs},
author = {Gordon F. Royle and Alan D. Sokal},
journal= {arXiv preprint arXiv:1307.1721},
year = {2020}
}