Arboricity: An acyclic hypergraph decomposition problem motivated by database theory

Authors:
Yeow Meng Chee;Lijun Ji;Andrew Lim;Anthony K. H. Tung
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu, China;Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong;Department of Computer Science, School of Computing, National University of Singapore, Singapore
Venue:
Discrete Applied Mathematics
Year:
2012

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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^-^@dn), @d positive, and determined exactly when k=n-3. This proves a conjecture of Wang (2008) [20] in the asymptotic sense.