论文信息 - Coverings of Pairs by Quintuples

Coverings of Pairs by Quintuples

Abstract Let 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.

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