Strong fractional choice number of series-parallel graphs

Abstract

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 $\mathcal{G}$ of graphs is the supremum of the strong fractional choice number of graphs in $\mathcal{G}$. We denote by ${\mathcal{Q}}_k$ 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 ${\mathcal{Q}}_k$ is exactly $2+\frac{1}{q}$.

7 pages