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Paths and cycles of hypergraphs 被引量:3

Paths and cycles of hypergraphs
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摘要 Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs are constructed. The systems suit the structure properties of relational databases. The concepts of pseudo cycles and essential cycles of hypergraphs are introduced. They are relative to each other. Whether a family of cycles of a hypergraph is dependent or independent is defined. An enumeration formula for the maximum number of independent essential cycles of a hypergraph is given. Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs are constructed. The systems suit the structure properties of relational databases. The concepts of pseudo cycles and essential cycles of hypergraphs are introduced. They are relative to each other. Whether a family of cycles of a hypergraph is dependent or independent is defined. An enumeration formula for the maximum number of independent essential cycles of a hypergraph is given.
出处 《Science China Mathematics》 SCIE 1999年第1期1-12,共12页 中国科学:数学(英文版)
关键词 HYPERGRAPH path connected CYCLE PSEUDO CYCLE ESSENTIAL cycle. hypergraph path connected cycle pseudo cycle essential cycle
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  • 1M Meszka,A Rosa.Decomposing complete 3-uniform hypergraph into Hamiltonian cycles. Australasian Journal of Combinatorics . 2009
  • 2Katona, Gyula Y.,Kierstead, H.A.Hamiltonian chains in hypergraphs. Journal of Geography . 1999
  • 3(美) 沙特朗 (Chartrand,G.),(美) 张萍,著.图论导引(M)人民邮电出版社, 2007
  • 4Robert F. Bailey,Brett Stevens.??Hamiltonian decompositions of complete k -uniform hypergraphs(J)Discrete Mathematics . 2009 (22)
  • 5Baoguang Xu,Jianfang Wang.??On the Hamiltonian cycle Decompositions of Complete 3-Uniform Hypergraphs(J)Electronic Notes in Discrete Mathematics . 2002
  • 6Helen Verrall.Hamilton decompositions of complete 3-uniform hypergraphs. Discrete Mathematics . 1994
  • 7Jirimutu,Wang Jianfang.??Hamiltonian decomposition of complete bipartite r -hypergraphs(J)Acta Mathematicae Applicatae Sinica . 2001 (4)
  • 8Jianfang Wang,Tony T. Lee.??Paths and cycles of hypergraphs(J)Science in China Series A: Mathematics . 1999 (1)
  • 9吉日木图,王建方.HAMILTONIAN DECOMPOSITION OF COMPLETE BIPARTITE γ-HYPERGRAPHS[J].Acta Mathematicae Applicatae Sinica,2001,17(4):563-566. 被引量:4
  • 10王建方,闫桂英.超图的圈结构[J].科学通报,2001,46(19):1585-1589. 被引量:8

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