Choosability Of Bipartite Graphs

Let \(n(k)\) be the smallest number of vertices of a bipartite graph not being \(k\)-choosable. We show that \(n(3) = 14\) and moreover that \(n(k) \leq k. n(k-2)+2^k\). In particular, it follows that \(n(4) \leq 40\) and \(n(6) \leq 304\).