Geodesic
The size of minimum 3-trees: cases 0 and 1 mod 12
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 177-187

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A 3-uniform hypergraph is called a minimum 3-tree, if for any 3-coloring of its vertex set there is a heterochromatic triple and the hypergraph has the minimum possible number of triples. There is a conjecture that the number of triples in such 3-tree is ⎡(n(n-2))/3⎤ for any number of vertices n. Here we give a proof of this conjecture for any n ≡ 0,1 mod 12.
Keywords: tight hypergraphs, triple systems 
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Arocha, Jorge; Tey, Joaquín. The size of minimum 3-trees: cases 0 and 1 mod 12. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 177-187. http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a12/