A maximal zero-free interval for chromatic polynomials of bipartite planar graphs

Abstract

It is well known that (- ∞, 0) and (0, 1) are two maximal zero-free intervals for all chromatic polynomials. Jackson [A zero-free interval for chromatic polynomials of graphs, Combin. Probab. Comput. 2 (1993), 325-336] discovered that (1, frac(32, 27)] is another maximal zero-free interval for all chromatic polynomials. In this note, we show that (1, frac(32, 27)] is actually a maximal zero-free interval for the chromatic polynomials of bipartite planar graphs. © 2007 Elsevier B.V. All rights reserved.