Decomposition of bi-colored square arrays into balanced diagonals

Given an n×n array M (n≥7), where each cell is colored in one of two colors, we give a necessary and sufficient condition for the existence of a partition of M into n diagonals, each containing at least one cell of each color. As a consequence, it follows that if each color appears in at least 2n−1 cells, then such a partition exists. The proof uses results on completion of partial Latin squares.