On zero-free intervals in (1, 2) of chromatic polynomials of some families of graphs

Abstract

For a family S of graphs, let ω(S) be the supremum of t :1 < t ≤ 2 such that P(G, λ) ≠ 0 for all G εS and all λ ε (1,t). In this paper we show that ω(S) = ω(S ∩ κ) for any family S of graphs satisfying certain conditions, where κ is a special family of graphs. This result makes it much easier to determine ω(S) for such families S. © 2010 Society for Industrial and Applied Mathematics.