On a theorem of J. Ossowski (Q1356025)

Let \(M\) be a zero-one matrix containing at most \(n\) ones in each row and fewer then \((k+1)n\) ones in all. Then, for any minimal set \(C\) of columns such that deleting those columns the remaining matrix contains no \(r \times (n-r+1)\) submatrix of ones for \(r=1,\ldots,n,\) \(C\) has cardinality at most \(k.\) This theorem is a slight generalization of an earlier result of J. Ossowski which solved a problem of the author.