Regions Without Complex Zeros for Chromatic Polynomials on Graphs with Bounded Degree

Abstract

We prove that the chromatic polynomial $P_\mathbb{G}(q)$ of a finite graph $\mathbb{G}$ of maximal degree Δ is free of zeros for | q | ≥ C *(Δ) with This improves results by Sokal and Borgs. Furthermore, we present a strengthening of this condition for graphs with no triangle-free vertices.