# Dinitz conjecture

The Dinitz theorem is closely related to graph theory, in which it can be succinctly stated as ${\displaystyle \chi _{l}^{\prime }(K_{n,n})=n}$ for natural ${\displaystyle n}$. It means that the list chromatic index of the complete bipartite graph ${\displaystyle K_{n,n}}$ equals ${\displaystyle n}$. In fact, Fred Galvin proved the Dinitz theorem as a special case of his theorem stating that the list chromatic index of any bipartite multigraph is equal to its chromatic index. Moreover, it is also a special case of the edge list coloring conjecture saying that the same holds not only for bipartite graphs, but also for any loopless multigraph.