On chromatic roots of large subdivisions of graphs Original Research Article

Given a graph G, we derive an expression for the chromatic polynomials of the graphs resulting from subdividing some (or all) of its edges. For special subfamilies of these, we are able to describe the limits of their chromatic roots. We also prove that for any ε>0, all sufficiently large subdivisions of G have their chromatic roots in |z−1|<1+ε. A consequence of our work will be a characterization of the graphs having a subdivision whose chromatic polynomial has a root with negative real part.