Given a minor-closed class of graphs G, what is the infimum of
the non-trivial roots of the chromatic polynomial of G∈G? When
G is the class of all graphs, the answer is known to be 32/27. We
answer this question exactly for three minor-closed classes of graphs.
Furthermore, we conjecture precisely when the value is larger than 32/27.Comment: 18 pages, 5 figure