The size of minimum 3-trees

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 l n(n−2) 3 m for any number of vertices n. Here we give a proof of this conjecture for any n ≡ 0, 1 mod 12.

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: Jorge L. Arocha, Joaquín Tey
• Keywords: 3-uniform Hypergraph, Heterochromatic Triple, JGT 2007, Minimum Possible Number