Choosability Of Bipartite Graphs

Abstract

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 $n(k)\le k.n(k-2)+2^k$. In particular, it follows that $n(4)\le 40$ and $n(6)\le 304$.