ON ACYCLIC AND CYCLIC HYPERGRAPHS
Wang, Jian-fang, Li, Haizhu · 系统科学与复杂性：英文版 · 2002
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.