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 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.
