On the location of chromatic zeros of series-parallel graphs

In this paper we consider the zeros of the chromatic polynomial of series-parallel graphs. Complementing a result of Sokal, giving density outside the disk |q−1|≤1, we show density of these zeros in the half plane R(q)>3/2 and we show there exists an open region U containing the interval (0,32/27) such that U∖{1} does not contain zeros of the chromatic polynomial of series-parallel graphs.
We also disprove a conjecture of Sokal by showing that for each large enough integer Δ there exists a series-parallel graph for which all vertices but one have degree at most Δ and whose chromatic colynomial has a zero with real part exceeding Δ.