Acyclic hypergraphs are analogues of forests in graphs. They arevery useful in the design of databases. The number of distinct acyclic uniform hypergraphs with n labeled vertices is studied. With the aid of the princi...Acyclic hypergraphs are analogues of forests in graphs. They arevery useful in the design of databases. The number of distinct acyclic uniform hypergraphs with n labeled vertices is studied. With the aid of the principle of inclusion-exclusion, two formulas are presented. One is the explicit formula for strict (d)-connected acyclic hypergraphs, the other is the recurrence formula for linear acyclic hypergraphs.展开更多
Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform ac...Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform acyclic hypergraphs of order n is shown to be展开更多
So far,the acyclic hypergraph has two different definitions.One is based on the cyclomatic number of the hypergraph,whereas the other arises from the acyclic schema of the relational database in the computer science.I...So far,the acyclic hypergraph has two different definitions.One is based on the cyclomatic number of the hypergraph,whereas the other arises from the acyclic schema of the relational database in the computer science.In this paper,it is first proved that these two definitions coincide with each other completely.Then we prove that a hypergraph H is not acyclic,or cyclic,if and only if it contains a special partial hypergraph named hypercircuit.In addition,we show that H has l(H) different hypercircuits,where l(H)is a parameter used to decide whether H is acyclic or cyclic.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19831080) .
文摘Acyclic hypergraphs are analogues of forests in graphs. They arevery useful in the design of databases. The number of distinct acyclic uniform hypergraphs with n labeled vertices is studied. With the aid of the principle of inclusion-exclusion, two formulas are presented. One is the explicit formula for strict (d)-connected acyclic hypergraphs, the other is the recurrence formula for linear acyclic hypergraphs.
基金Supported by the National Natural Science Foundation of China (No.19831080)
文摘Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum γ-uniform acyclic hypergraphs of order n is shown to be
基金This research is supported by the National Natural Science Foundation of China(No. 19831080).
文摘So far,the acyclic hypergraph has two different definitions.One is based on the cyclomatic number of the hypergraph,whereas the other arises from the acyclic schema of the relational database in the computer science.In this paper,it is first proved that these two definitions coincide with each other completely.Then we prove that a hypergraph H is not acyclic,or cyclic,if and only if it contains a special partial hypergraph named hypercircuit.In addition,we show that H has l(H) different hypercircuits,where l(H)is a parameter used to decide whether H is acyclic or cyclic.
