The strong fractional choice number of a graph $G$ is the infimum of those real numbers $r$ such that $G$ is $(\lceil rm \rceil, m)$-choosable for every positive integer $m$. The strong fractional choice number of a family ${\cal G}$ of graphs is the supremum of the strong fractional choice number of graphs in ${\cal G}$. We denote by ${\cal{Q}}_k$ the class of series-parallel graphs with girth at least $k$. This paper proves that for $k=4q-1, 4q,4q+1, 4q+2$, the strong fractional number of ${\cal{Q}}_k$ is exactly $2+ \frac{1}{q}$.

中文翻译：

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串并图的强分数选择数

图 $G$ 的强分数选择数是那些实数 $r$ 的下界，使得 $G$ 对于每个正整数 $m$ 都是 $(\lceil rm \rceil, m)$-choosable。图族${\cal G}$的强分数选择数是${\cal G}$中图的强分数选择数的上界。我们用 ${\cal{Q}}_k$ 表示周长至少为 $k$ 的串并图类。本文证明对于$k=4q-1, 4q,4q+1, 4q+2$，${\cal{Q}}_k$的强小数正好是$2+ \frac{1}{q} $.