Geodesic
On the Size of a Maximum Transversal in a Steiner Triple System
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1202-1204

Voir la notice de l'article provenant de la source Cambridge University Press

Let (X, ) be a Steiner triple system on v = |X| points, and suppose that is a partial parallel class (transversal, clear set, set of pairwise disjoint blocks) of maximum size . We want to derive a bound on . (I conjecture that in fact r is bounded, e.g., r ≦ 4 – 4 is attained for the Fano plane, but all that has been proved so far (cf. [1], [2]) are bounds r < C.v for some C. Here we shall prove r < 5v 2/3.)Define a sequence of positive real numbers by q 0 = Q · r 2/v, , where l is determined by ql ≧ 6, , i.e., (The constant Q will be chosen later.) Define inductively sets Ai , Ki and collections as follows. Let 
Brouwer, A. E. On the Size of a Maximum Transversal in a Steiner Triple System. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1202-1204. doi: 10.4153/CJM-1981-090-7
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[1] 1. Lindner, C. C. and Phelps, K. T., A note on partial parallel classes in Steiner systems, Discr. Math. 24 (1978), 109–112. Google Scholar

[2] 2. Wang, S. P., On self orthogonal Latin squares and partial transversals of Latin squares, Ph.D. thesis, Ohio State University, Columbus, Ohio (1978). Google Scholar

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