A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks axe regarded as ordered k-tuples and in which each ordered pair of elements occurs in at least λ blocks. Let DE(v, k, λ) denote the minimum number of blocks in a DC(v, k, λ). In this paper the values of the function DE(v, k, λ) are determined for all odd integers v ≥ 5 and λ odd, with the exception of (v, λ) = (53, 1), (63, 1), (73, 1), (83, 1). Further, we provide an example of a covering design that can not be directed.
|Number of pages||19|
|Journal||Journal of Combinatorial Mathematics and Combinatorial Computing|
|State||Published - Aug 2008|