The size of minimum 3-trees: Cases 3 and 4 mod 6

A 3-uniform hypergraph is called a minimum 3-tree, if for any 3-coloring of its vertex set there is a heterochromatic edge and the hypergraph has the minimum possible number of edges. Here we show that the number of edges in such S-tree is inverted right perpendicular n(n-2)/3 inverted left perpendicular for any number of vertices n = 3, 4 (mod 6). (C) 1999 John Wiley & Sons, Inc. J Graph Theory 30: 157-166, 1999.