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Let \,H^{0} and \,H^{1} be hypergraphs with the same vertex set \,V. An ordered pair \,H = (H^{0},H^{1}) is called a bihypergraph with the set of 0-edges \,E(H^{0}) and the set of 1-edges \,E(H^{1}). Every hyperedge of either \,H^{0} or \,H^{1} is considered as a hyperedge of \,H. The order of \,H is \,n(H) = |V|. The rank of \,H is \,r(H) = \max\{r(H^{0}), r(H^{1})\}.

A bihypergraph \,H = (H^{0}, H^{1}) is called bipartite if there exists an ordered partition V^{0} \cup V^{1} = V(H) (bipartition) such that the set \,V^{i} is stable in \,H^{i}, \,i = 0,1.


  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.