In this paper we consider the zeros of the chromatic polynomial of series-parallel graphs. Complementing a result of Sokal, showing density outside the disk $|q-1|\leq1$, we show density of these zeros in the half plane $\Re(q)>3/2$ and we show there exists an open region $U$ containing the interval $(0,32/27)$ such that $U\setminus\{1\}$ 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 $\Delta$ there exists a series-parallel graph for which all vertices but one have degree at most $\Delta$ and whose chromatic polynomial has a zero with real part exceeding $\Delta$.

翻译：本文研究了串并联图染色多项式的零点。作为对Sokal关于圆盘$|q-1|\leq1$外部零点稠密性结果的补充，我们证明了这些零点在半平面$\Re(q)>3/2$内稠密，并指出存在一个包含区间$(0,32/27)$的开区域$U$，使得$U\setminus\{1\}$不包含串并联图染色多项式的零点。此外，我们通过证明对任意足够大的整数$\Delta$，存在一个除一个顶点外其余顶点度数均不超过$\Delta$的串并联图，其染色多项式具有实部超过$\Delta$的零点，从而否证了Sokal的一个猜想。