The size of minimum 3‐trees
Jorge L. Arocha, Joaquín Tey · Journal of Graph Theory · 2006
Abstract A 3‐uniform hypergraph (3‐graph) is said to be tight, if for any 3‐partition of its vertex set there is a transversal triple. We give the final steps in the proof of the conjecture that the minimum number of triples in a tight 3‐graph on n vertices is exactly $\left\lceil n(n-2)/3 \right\rceil$ . © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 103–114, 2007