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,t1​], where t1​≈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 t1​
from above. We employ the Whitney 2-switch operation to manage the analysis
of an infinite class of chromatic polynomials.Comment: 16 pages, 5 figure