Weighted coverings and packings

Highly Saturated Packings and Reduced Coverings

We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the closure of its interior. A packing P with congruent replicas of a body K is n-saturated if no n− 1 members of it can be replaced with n replicas of K, and it is completely saturated if it is n-saturated for each n ≥ 1....

Finite Sphere Packings and Sphere Coverings

Packings and coverings in directed graphs

On 2-Coverings and 2-Packings of Laminar Families

Let H be a laminar family of subsets of a groundset V A k cover of H is a multiset C of edges on V such that for every subset S in H C has at least k edges that have exactly one end in S A k packing of H is a multiset P of edges on V such that for every subset S in H P has at most k u S edges that have exactly one end in S Here u assigns an integer capacity to each subset in H Our main results ...

Constructions of uniform designs by using resolvable packings and coverings

In this paper, uniform designs are constructed based on nearly U-type designs and the discrete discrepancy. The link between such uniform designs and resolvable packings and coverings in combinatorial design theory is developed. Through resolvable packings and coverings without identical parallel classes, many infinite classes of new uniform designs are then produced.