The Packing Property
Journal Article - Open Access
Carnegie Mellon University Pittsburgh United States
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A clutter VE packs if the smallest number of vertices needed to intersect all the edges i.e. a minumum transversal is equal to the maximum number 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 minors pack. An m n 0,1 matrix is minimally nonpacking if it is the edge-vertex incidence matrix of a minimally nonpacking clutter. Minimally nonpacking matrices can be viewed as the counterpart for the set covering problem of minimally imperfect matrices for the set packing problem. This paper proves several properties of minimally nonpacking clutters and matrices.
- Numerical Mathematics