Balanced list edge-colourings of bipartite graphs

Galvin solved the Dinitz conjecture by proving that bipartite graphs are Δ-edge-choosable. We employ Galvinʹs method to show some further list edge-colouring properties of bipartite graphs. In particular, there exist balanced list edge-colourings for bipartite graphs. In the light of our result, it is a natural question whether a certain generalization of the well-known list colouring conjecture is true.