The strong fractional choice number of 3‐choice‐critical graphs

A graphG$G$ is called 3‐choice‐critical ifG$G$ is not 2‐choosable but any proper subgraph ofG$G$ is 2‐choosable. A graphG$G$ is strongly fractionalr$r$ ‐choosable ifG$G$ is( a , b )$(a,b)$ ‐choosable for all positive integersa , b$a,b$ for whicha ∕ b ≥ r$a\unicode{x02215}b\ge r$ . The strong fractional choice number ofG$G$ isc h f s ( G ) = inf {r : G$c{h}_{f}^{s}(G)=\text{inf}\{r:G$ is strongly fractionalr$r$ ‐choosable}$\}$ . This paper determines the strong fractional choice number of all 3‐choice‐critical graphs.