Arboricity: An acyclic hypergraph decomposition problem motivated by database theory

Abstract

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 ( log 1 − δ n ) , δ positive, and determined exactly when k = n − 3 . This proves a conjecture of Wang (2008) [20] in the asymptotic sense.