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 , 32 27 ] is another maximal zero-free interval for all chromatic polynomials. In this note, we show that ( 1 , 32 27 ] is actually a maximal zero-free interval for the chromatic polynomials of bipartite planar graphs.