A perfect covering of a v-set X is a set of subsets of X (called blocks), such that every pair of elements of X (points) occurs in a unique block. A perfect covering is also referred to in the literature as a pairwise balanced design or a finite linear space. The quantity of g’“‘(v) is defined to be the minimum number of blocks in a perfect covering of a v-set, in which the longest block has si...

A (v, k, t) covering design, or covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering’s size, and the minimum size of such a covering is denoted by C(v, k, t). This paper gives three new methods for constructing good coverings: a greedy algorithm similar to Conway and Sloan...

This short paper introduces a method for verifying equivalence classes for module/unit testing. This is achieved using a two-layer covering array, in which some or all values of a primary covering array represent equivalence classes. A second layer covering array of the equivalence class values is computed, and its values substituted for the equivalence class names in the primary array. It is s...

We determine, for each v == 1 mod 3, the maximum (resp. minimum) number of near-triangle factors possible on v points so that each pair of distinct points occurs in a triple in at most (resp. at least) one of the neartriangle factors. In particular, we show that for each v == 1 mod 3, v:/: 7, there exists a near-resolvable exact 2-covering of v points by triples whose near-triangle factors admi...

We prove that an equivalent condition for a uniform space to be cov-erable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to find covering entourage, (2) correct an error in [3], and (3) show that coverable is equivalent to chain connected and uniformly joinable in the sense of [5...

A simple graph G = (V (G), E(G)) admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. An (a, d)-H-antimagic total labeling of G admitting an H-covering is a bijective function ξ : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for all subgraphs H ′ isomorphic to H, the H-weights w(H ′) = ∑