Chromatic properties of hamiltonian graphs

We study the problem of the location of real zeros of chromatic polynomials for some families of graphs. In particular, a problem presented by Thomassen (see [On the number of hamiltonian cycles in bipartite graphs, Combin. Probab. Comput. 5 (1996) 437–442.]) is discussed and a result for hamiltonian graphs is presented. An open problem is stated for 2-connected graphs with a hamiltonian path.