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Directed Covering with Block Size 5 and Index Odd

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Abstract

A directed covering design, DC(v, k, λ), is a (v, k, 2λ) covering design in which the blocks are 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 DC(v, 5, λ) are determined for all even integers v ≥ 5 and λ odd.

References (28)

  • R.J. Abel

    Four MOLS of order 28 and 52

    J. Combin. Theory Ser. A

    (1991)
  • R.J. Abel et al.

    Four MOLS of orders 20, 30, 38 and 44

    J. Combin. Theory Ser. A

    (1993)
  • R.J. Abel, A.E. Brouwer, C.J. Colbourn, J.H. Dinitz, Mutually Orthogonal Latin Square, in: CRC Handbook of...
  • A.M. Assaf

    An application of modified group divisible designs

    J. Combin. Theory Ser. A

    (1994)
  • A.M. Assaf

    On packing designs with block size 5 and index 7 ≤ λ ≤ 21

    JCMCC

    (1998)
  • A.M. Assaf

    Bipacking pairs by quintuples: The case v ≡ 13 (mod 20)

    Discrete Math

    (1994)
  • A.M. Assaf

    On directed packing designs with block size 5 and index 2

    Utilitas Math

    (1996)
  • A.M. Assaf

    Directed covering with block size 5 and index even

    Discrete Math

    (1998)
  • A.M. Assaf et al.

    On tricovers of pairs by quintuples: V≡ (1 mod 4)

    Ars Combinatoria

    (1992)
  • A.M. Assaf et al.

    On covering designs with block size 5 and index 4

    Ars Combinatoria

    (1992)
  • A.M. Assaf et al.

    Directed packing with block size 5 and odd v

    Australasian J. Of Comb

    (1996)
  • A.M. Assaf, N. Shalaby, J. Yin, Directed packing and covering designs with block size 4, Discrete Math.,...
  • F. Bennet et al.

    Directed group divisible designs

    Journal of Comb. Designs

    (1998)

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