Bipartite graphs are $(\frac{4}{5}-\varepsilon) \frac{\Delta}{\log
\Delta}$-choosable
Bipartite graphs are $(\frac{4}{5}-\varepsilon) \frac{\Delta}{\log
\Delta}$-choosable
Alon and Krivelevich conjectured that if $G$ is a bipartite graph of maximum degree $\Delta$, then the choosability (or list chromatic number) of $G$ satisfies $\chi_{\ell}(G) = O \left ( \log \Delta \right )$. Currently, the best known upper bound for $\chi_{\ell}(G)$ is $(1 + o(1)) \frac{\Delta}{\log \Delta}$, which also …