The size of minimum 3-trees

  • Authors:
  • Jorge L. Arocha;Joaquín Tey

  • Affiliations:
  • Instituto de Matemáticas, Unam Ciudad Universitaria, Circuito Exterior, México D.F. 04510;Departamento de Matemáticas, Uam-Iztapalapa Ave. Sn. Rafael Atlixco #186, Col. Vicentina, México D.F. 09340

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2007

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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 Dedicated to the memory of Victor Neumann-Lara.