The minimum independence number for designs


Fort=2,3 andk≥2t−1 we prove the existence oft−(n,k,λ) designs with independence numberC λ,k n (k−t)/(k−1) (ln n) 1/(k−1). This is, up to the constant factor, the best possible.

Some other related results are considered.

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  1. [1]

    T. Beth, D. Jungnickel, andH. Lenz:Design Theory, Cambridge University Press, Cambridge, 1986.

    Google Scholar 

  2. [2]

    M. de Brandes, andV. Rödl: Steiner triple systems with small maximal independent sets,Ars Combinatoria 17 (1984), 15–19.

    Google Scholar 

  3. [3]

    J. Brown, andV. Rödl: A Ramsey type problem concerning vertex colorings,J. Comb. Theory, Series B 52 (1991), 45–52.

    Google Scholar 

  4. [4]

    N. Eaton andV. Rödl: A canonical Ramsey theorem,Rand. Struc. Alg. 3 (1992), 427–444.

    Google Scholar 

  5. [5]

    P. Frankl, V. Rödl, andR. M. Wilson: The number of submatrices of a given type in a Hadamard matrix and related results,J. Comb. Theory, Series B 44 (1988), 317–328.

    Google Scholar 

  6. [6]

    Z. Füredi: Maximal independent subsets in Steiner systems and in planar sets,SIAM J. Disc. Math 4 (1991), 196–199.

    Google Scholar 

  7. [7]

    J. W. P. Hirschfeld:Projective Geometries over Finite Fields, Clarendon Press, Oxford, 1979.

    Google Scholar 

  8. [8]

    K. T. Phelps, andV. Rödl: Steiner triple systems with minimum independence number,Ars Combinat. 21 (1986), 167–172.

    Google Scholar 

  9. [9]

    V. Rödl, andE. Šiňajová Note on independent sets in Steiner systems,Random Structures and Algorithms 5 (1994), 183–190.

    Google Scholar 

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Supported by NSF Grant DMS-9011850

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Grable, D.A., Phelps, K.T. & Rödl, V. The minimum independence number for designs. Combinatorica 15, 175–185 (1995).

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Mathematics Subject Classification (1991)

  • 05 B 05