In this paper we obtain a partial answer in graph-theoretic form to a question raised by Ryser (2, p. 68) concerning the minimal number of interchanges required to transform equivalent (0, l)-matrices into each other.For given positive integersmandnwe consider the collection ofm×n(0, 1)-matricesA= {aij}, i.e.aij= 0 or 1 for 1 ≤i≤m, 1 ≤j≤n. We say the (0, 1)-matricesA= {aij} andB= {bij} areequivalentand writeA~Bif and only if they have the same row and column sums, that is, if and only if.