A clutter (V, E) packs if the smallest number of vertices needed to interse
ct all the edges (i.e. a minimum transversal) is equal to the maximum numbe
r of pairwise disjoint edges (i.e. a maximum matching). This terminology is
due to Seymour 1977. A clutter is minimally nonpacking if it does not pack
but all its miners pack. An m x n 0,1 matrix is minimally nonpacking if it
is the edge-vertex incidence matrix of a minimally nonpacking clutter. Min
imally nonpacking matrices can be viewed as the counterpart for the set cov
ering problem of minimally imperfect matrices for the set packing problem.
This paper proves several properties of minimally nonpacking clutters and m
atrices.