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.