An extension of Stein-Lovász theorem and some of its applications

The Stein-Lovász theorem provides an algorithmic way to deal with the existence of certain good coverings, and thus offers bounds related to some combinatorial structures. An extension of the classical Stein-Lovász theorem for multiple coverings is given, followed by some applications for finding upper bounds of the sizes of (d, s out of r; z]-disjunct matrices and (k, m, c, n; z)selectors, respectively. This gives a unified treatment for some previously known results relating to various models of group testing.