Editing Hypergraph (section)

===Berge cycles===
A first notion of cycle was introduced by [[Claude Berge]]<ref>{{cite book |first=Claude |last=Berge |title=Graphs and Hypergraphs |location=Amsterdam |publisher=North-Holland |year=1973 |isbn=0-7204-2450-X }}</ref>. A '''Berge cycle''' in a hypergraph is an alternating sequence of distinct vertices and edges <math>(v_1, e_1, \dots , v_n, e_n)</math> where <math>v_i, v_{i+1}</math> are both in <math>e_i</math> for each <math>i \in [n]</math> (with indices taken modulo <math>n</math>).

Under this definition a hypergraph is '''acyclic''' if and only if its [[incidence graph]] (the [[bipartite graph]] defined above) is acyclic. Thus Berge-cyclicity can obviously be tested in [[linear time]] by an exploration of the incidence graph.