C. Thomassen, The zero-free intervals for chromatic polynomials of graphs, MAT-REPORT NO. 1995-18, Mathematical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark, 13 pages.
Abstract: The maximal zero-free intervals for chromatic polynomials are precisely (-∞,0) , (0,1) , (1, 32/27). More generally, the zeros of chromatic polynomials of graphs of tree-width at most k consist of 0, 1 and a dense subset of the interval (32/27,k]. We also prove that, for every family F of graphs closed under minors (and not consisting of all graphs) there exists a constant c such that the interval (c, infinity) contains no zeros of chromatic polynomials of graphs in F. For the families of graphs not embeddable in the projective plane or not embeddable in the torus the best possible values for c are 5 and 6, respectively.
December, 1995 Bjarne Toft