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→无环性 Acyclicity
In contrast with ordinary undirected graphs for which there is a single natural notion of [[cycle (graph theory)|cycles]] and [[Forest (graph theory)|acyclic graphs]], there are multiple natural non-equivalent definitions of acyclicity for hypergraphs which collapse to ordinary graph acyclicity for the special case of ordinary graphs.
In contrast with ordinary undirected graphs for which there is a single natural notion of [[cycle (graph theory)|cycles]] and [[Forest (graph theory)|acyclic graphs]], there are multiple natural non-equivalent definitions of acyclicity for hypergraphs which collapse to ordinary graph acyclicity for the special case of ordinary graphs.
与只有'''圈 cycle'''和'''森林 forest'''的普通无向图相比，对于超图的特殊情形，那些坍缩为平凡图的无环性超图有多种自然不等价的'''无环性 acyclicity''' 定义。
与只有'''圈 cycle'''和'''森林 forest'''的普通无向图相比，对于超图的特殊情形，那些坍缩为普通图的无环性超图有多种自然不等价的'''无环性 acyclicity''' 定义。
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.