Roots of chromatic polynomials Original Research Article

The chromatic polynomial P(G,λ) of a graph G of order n, size m and chromatic number χ has a root with modulus at least [m−(χ2)]/(n−χ). It is proved that this bound is the best possible for (χ−1)-trees only. Moreover, a sufficient condition for complex roots of P(G,λ) is presented. These results are an extension of those presented by J. Brown in the paper On the Roots of Chromatic Polynomials, J. Combin. Theory, Ser. B 72 (1998) 251.