Linear bound in terms of maxmaxflow for the chromatic roots of series-parallel graphs

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

References in corpus (5)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights
• The Brown-Colbourn conjecture on zeros of reliability polynomials is false
• Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids
• Maxmaxflow and counting subgraphs

Cited by in corpus (2)

• Location of zeros for the partition function of the Ising model on bounded degree graphs
• The Beraha number $B_{10}$ is a chromatic root