Problem 629

Erdős Problem #629: declared status 'open'. Formalized: no. The list chromatic number $\chi_L(G)$ is defined to be the minimal $k$ such that for any assignment of a list of $k$ colours to each vertex of $G$ (perhaps different lists for different vertices) a colouring of each vertex by a colour on its list can be chosen such that adjacent vertices receive distinct colours. Determine the minimal number of vertices $n(k)$ of a bipartite graph $G$ such that $\chi_L(G)>k$. Prize: no. Tags: chromatic number, graph theory.