The strong fractional choice number of $3$-choice critical graphs

Abstract

A graph $G$ is called $3$-choice critical if $G$ is not $2$-choosable but any proper subgraph is $2$-choosable. A graph $G$ is strongly fractional $r$-choosable if $G$ is $(a,b)$-choosable for all positive integers $a,b$ for which $a/b \ge r$. The strong fractional choice number of $G$ is $ch_f^s(G) = \inf \{r: G $ is strongly fractional $r$-choosable$\}$. This paper determines the strong fractional choice number of all $3$-choice critical graphs.