On the zero-free region for the chromatic polynomial of claw-free graphs with and without induced square and induced diamond

Paula M. S. Fialho, Aldo Procacci

Given a claw-free graph $G=(V,E)$ with maximum degree $\hat{I}”$, we define the parameter $\hat{I}º\in [0,1]$ as $\hat{I}º=\frac{{\max }_{v\in V}|I_v|}{\lfloor \hat{I}{”}^2/4\rfloor }$ where $I_v$ is the set of a…