Coverings of Pairs by Quintuples

AbstractLet V be a finite set of ν elements. A covering of the pairs of V by k-subsets is a family F of k-subsets of V called blocks, such that each pair in V occurs in at least one member of F. For fixed ν and k, the covering problem is to determine the number of blocks in any minimum (as opposed to minimal) covering. We will denote the number of blocks in any minimum covering by C(v, k, 2). In this paper, we show that C(v, 5, 2) can be determined for v ≡ 1 and 2 modulo 4 with a lower bound on ν