# Bihypergraph

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Bihypergraphбигиперграф.

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 $\,H^{i}$, $\,i = 0,1$.

## Литература

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