Directed covering with block size 5 and v and λ Odd

Omar A. AbuGhneim, Hasan A. Al-Halees, Ahmed M. Assaf

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)237-255
Number of pages19
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
StatePublished - Aug 2008


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