2105.03304May 7, 2021Eq (2.4) is not correct and as such this invalidates Theorem 2.3 and consequently all the claimed results on the modulus of the zeros of chromatic polynomial. As fas as we can tell the results for the edge based block polynomials are correct (this concerns Sections 4 and 5). We will probably resubmit this part as part of a new paper at some point in the future

Improved bounds for zeros of the chromatic polynomial on bounded degree graphs

Maurizio Moreschi, Viresh Patel, Guus Regts, Ayla Stam

Combinatorics

arXiv PDF

Abstract

We prove that for any graph $G$ of maximum degree at most $Δ$ , the zeros of its chromatic polynomial $χ_G(z)$ (in $\mathbb{C}$ ) lie outside the disk of radius $5.02 Δ$