Towards a solution of the Dinitz problem? (Q1118600)

The Dinitz problem may be stated as follows: Given an \(m\times m\) array of m-sets, is it always possible to choose one element from each set so that the chosen elements are distinct in each row and column? Using some elementary properties of graph theory, the author partially resolves this problem by proving that if L is an \(r\times n\) array of n-sets with \(r\leq (2n)/7\), then L contains an \(r\times n\) Latin rectangle.