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 $\Delta$, we define the parameter $\kappa \in [0,1]$ as $\kappa =\frac{{\max }_{v\in V}|I_v|}{\lfloor {\Delta }^2/4\rfloor }$ where $I_v$ is the set of all i…