Arboricity : an acyclic hypergraph decomposition problem motivated by database theory

• Main Authors: Chee, Yeow Meng, Ji, Lijun, Lim, Andrew, Tung, Anthony K. H.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/99517; http://hdl.handle.net/10220/10864
• Institution: Nanyang Technological University

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