A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees

摘要

It is proved that if G is a graph containing a spanning tree with at most three leaves, then the chromatic polynomial of G has no roots in the interval (1, t(1)], where t(1) approximate to 1.2904 is the smallest real root of the polynomial (t-2)(6)+4(t-1)(2)(t-2)(3)-(t-1)(4). We also construct a family of graphs containing such spanning trees with chromatic roots converging to t(1) from above. We employ the Whitney 2-switch operation to manage the analysis of an infinite class of chromatic polynomials. (C) 2016 Elsevier B.V. All rights reserved.