Arboricity: An acyclic hypergraph decomposition problem motivated by database theory

The arboricity of a hypergraph H is the minimum number of acyclic hypergraphs that partition H . The determination of the arboricity of hypergraphs is a problem motivated by database theory. The exact arboricity of the complete k-uniform hypergraph of order n is previously known only for k ∈ {1, 2, n − 2, n − 1, n}. The arboricity of the complete k-uniform hypergraph of order n is determined asymptotically when k = n − O(log1−δ n), δ positive, and determined exactly when k = n − 3. This proves a conjecture of Wang (2008) [20] in the asymptotic sense. © 2011 Elsevier B.V. All rights reserved.