Geodesic
Maximal Subsets of a given Set having No Triple in Common with a Steiner Triple System on the set
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 777-778

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DOI

Let E be a finite set containing n elements, n ≡ 1, 3 (mod 6), S = S(E) a Steiner triple system on E, i.e. each unordered pair of elements of E is a subset of exactly one triple in S. Let T be a subset of E such that none of the triples of elements of T is a member of S. Erdös has asked (in a recent letter to the authors) for the maximal size of such a set T. Denote max |T| for fixed n and S by f(n, S). We prove in this note the following result: (i) (ii) for every n ≡ 1, 3 (mod 6) there exists a Steiner triple system S0 such that equality holds in i. 
Sauer, N.; Schönheim, J. Maximal Subsets of a given Set having No Triple in Common with a Steiner Triple System on the set. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 777-778. doi: 10.4153/CMB-1969-100-2
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     author = {Sauer, N. and Sch\"onheim, J.},
     title = {Maximal {Subsets} of a given {Set} having {No} {Triple} in {Common} with a {Steiner} {Triple} {System} on the set},
     journal = {Canadian mathematical bulletin},
     pages = {777--778},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-100-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-100-2/}
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