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A first definition of acyclicity for hypergraphs was given by [[Claude Berge]]:<ref>[[Claude Berge]], ''Graphs and Hypergraphs''</ref> a hypergraph is Berge-acyclic if its [[incidence graph]] (the [[bipartite graph]] defined above) is acyclic. This definition is very restrictive: for instance, if a hypergraph has some pair <math>v \neq v'</math> of vertices and some pair <math>f \neq f'</math> of hyperedges such that <math>v, v' \in f</math> and <math>v, v' \in f'</math>, then it is Berge-cyclic. Berge-cyclicity can obviously be tested in [[linear time]] by an exploration of the incidence graph.

A first definition of acyclicity for hypergraphs was given by [[Claude Berge]]:<ref>[[Claude Berge]], ''Graphs and Hypergraphs''</ref> a hypergraph is Berge-acyclic if its [[incidence graph]] (the [[bipartite graph]] defined above) is acyclic. This definition is very restrictive: for instance, if a hypergraph has some pair <math>v \neq v'</math> of vertices and some pair <math>f \neq f'</math> of hyperedges such that <math>v, v' \in f</math> and <math>v, v' \in f'</math>, then it is Berge-cyclic. Berge-cyclicity can obviously be tested in [[linear time]] by an exploration of the incidence graph.

由Claude Berge 给出了超图无环性的首个定义: <ref>Claude Berge,[https://www.amazon.com/Graphs-hypergraphs-North-Holland-mathematical-library/dp/0444103996 ''Graphs and Hypergraphs'']</ref> 如果它的'''关联图'''(上面定义的二部图)是无环的，则称这个超图是 Berge 无环的 Berge-acyclic。 这个定义是非常严格的：例如，假设一个超图有一些顶点<math>v \neq v'</math>和一些超边<math>f \neq f'</math> ，例如 <math>v, v' \in f</math> 和<math>v, v' \in f'</math>，那么它就是 Berge成环的 Berge-cyclic。 通过对关联图的探讨，Berge成环性 berge-cyclity可以在线性时间 linear time内得到有效验证 。

由Claude Berge 给出了超图无环性的首个定义: <ref>Claude Berge,[https://www.amazon.com/Graphs-hypergraphs-North-Holland-mathematical-library/dp/0444103996 ''Graphs and Hypergraphs'']</ref> 如果它的'''关联图'''(上面定义的二分图)是无环的，则称这个超图是 Berge 无环的 Berge-acyclic。 这个定义是非常严格的：例如，假设一个超图有一些顶点<math>v \neq v'</math>和一些超边<math>f \neq f'</math> ，例如 <math>v, v' \in f</math> 和<math>v, v' \in f'</math>，那么它就是 Berge成环的 Berge-cyclic。 通过对关联图的探讨，Berge成环性 berge-cyclity可以在线性时间 linear time内得到有效验证 。