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- W2078758420 abstract "Suppose S is a Steiner triple-system on the n-element set X, i.e., for every pair of distinct vertices of X there is exactly one triple in S containing them. Necessarily, |S| = n(n − 1)/6 holds. It is easy to see that, for S, T, S′, T′ ∈ S, S ∪ T = S′ ∪ T′ implies {S, T} = {S′, T′}. We show that, conversely, this condition, for any family S′ of 3-subsets of X, implies |S′| ⩽ n(n − 1)/6. A similar type of result is obtained for a weaker union condition. The corresponding problems for graphs are still open." @default.
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- W2078758420 date "1984-02-01" @default.
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- W2078758420 title "A new extremal property of Steiner triple-systems" @default.
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- W2078758420 doi "https://doi.org/10.1016/0012-365x(84)90183-3" @default.
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