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Maximal Subsets of a given Set having No Triple in Common with a Steiner Triple System on the set

Published online by Cambridge University Press:  20 November 2018

N. Sauer  and
J. Schönheim
N. Sauer
Affiliation:
The University of Calgary
J. Schönheim
Affiliation:
The University of Calgary
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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:

  1. (i)

  1. (ii) for every n ≡ 1, 3 (mod 6) there exists a Steiner triple system S0 such that equality holds in i.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 777 - 778
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Netto, Eugene, Lehrbuch der Combinatorik. Chelsea Publishing Company, New York, N.Y.Google Scholar