The Dinitz problem solved for rectangles

The Dinitz conjecture states that, for each n and for every collection of n-element sets ${S_{ij}}$, an $n \times n$ partial latin square can be found with the $(i,j){\text{th}}$ entry taken from ${S_{ij}}$. The analogous statement for $(n - 1) \times n$ rectangles is proven here. The proof uses a recent result by Alon and Tarsi and is given in terms of even and odd orientations of graphs.