Abstract
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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References
T. Beth, D. Jungnickel, andH. Lenz:Design Theory, Cambridge University Press, Cambridge, 1986.
M. de Brandes, andV. Rödl: Steiner triple systems with small maximal independent sets,Ars Combinatoria 17 (1984), 15–19.
J. Brown, andV. Rödl: A Ramsey type problem concerning vertex colorings,J. Comb. Theory, Series B 52 (1991), 45–52.
N. Eaton andV. Rödl: A canonical Ramsey theorem,Rand. Struc. Alg. 3 (1992), 427–444.
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.
Z. Füredi: Maximal independent subsets in Steiner systems and in planar sets,SIAM J. Disc. Math 4 (1991), 196–199.
J. W. P. Hirschfeld:Projective Geometries over Finite Fields, Clarendon Press, Oxford, 1979.
K. T. Phelps, andV. Rödl: Steiner triple systems with minimum independence number,Ars Combinat. 21 (1986), 167–172.
V. Rödl, andE. Šiňajová Note on independent sets in Steiner systems,Random Structures and Algorithms 5 (1994), 183–190.
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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). https://doi.org/10.1007/BF01200754
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DOI: https://doi.org/10.1007/BF01200754