Galvin's theorem

Statement

Galvin proved a considerably more general result: for every bipartite multigraph $G$,

$$\chi'_\ell(G) = \chi'(G).$$

By Kőnig's edge-coloring theorem the chromatic index of a bipartite multigraph equals its maximum degree, so $\chi'_\ell(G) = \Delta(G)$. Taking $G = K_{n,n}$ recovers the Dinitz theorem.