Bihypergraph: различия между версиями
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'''Bihypergraph''' | '''Bihypergraph''' — ''[[бигиперграф]].'' | ||
Let <math>H^{0}</math> and <math>H^{1}</math> be hypergraphs with the same vertex set <math>V</math>. | Let <math>\,H^{0}</math> and <math>\,H^{1}</math> be [[hypergraph|hypergraphs]] with the same [[vertex]] set <math>\,V</math>. | ||
An ordered pair <math>H = (H^{0},H^{1})</math> is called a '''bihypergraph''' | An ordered pair <math>\,H = (H^{0},H^{1})</math> is called a '''bihypergraph''' | ||
with the set of 0-edges <math>E(H^{0})</math> and the set of 1-edges <math>E(H^{1})</math>. | with the set of [[edge|0-edges]] <math>\,E(H^{0})</math> and the set of 1-edges <math>\,E(H^{1})</math>. | ||
Every hyperedge of either <math>H^{0}</math> or <math>H^{1}</math> is considered as a | Every hyperedge of either <math>\,H^{0}</math> or <math>\,H^{1}</math> is considered as a | ||
hyperedge of <math>H</math>. The order of <math>H</math> is <math>n(H) = |V|</math>. The rank of <math>H</math> | hyperedge of <math>\,H</math>. The order of <math>\,H</math> is <math>\,n(H) = |V|</math>. The [[rank of a graph|rank]] of <math>\,H</math> | ||
is <math>r(H) = \max\{r(H^{0}), r(H^{1})\}</math>. | is <math>\,r(H) = \max\{r(H^{0}), r(H^{1})\}</math>. | ||
A bihypergraph <math>H = (H^{0}, H^{1})</math> is called '''bipartite''' if there | A bihypergraph <math>\,H = (H^{0}, H^{1})</math> is called '''[[bipartite graph|bipartite]]''' if there | ||
exists an ordered partition <math>V^{0} \cup V^{1} = V(H)</math> (bipartition) | exists an ordered partition <math>V^{0} \cup V^{1} = V(H)</math> (bipartition) | ||
such that the set <math>V^{i}</math> is ''stable'' in <math>H^{i}</math>, <math>i = 0,1</math>. | such that the set <math>\,V^{i}</math> is ''stable'' in <math>\,H^{i}</math>, <math>\,i = 0,1</math>. | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 11:51, 17 января 2012
Bihypergraph — бигиперграф.
Let [math]\displaystyle{ \,H^{0} }[/math] and [math]\displaystyle{ \,H^{1} }[/math] be hypergraphs with the same vertex set [math]\displaystyle{ \,V }[/math]. An ordered pair [math]\displaystyle{ \,H = (H^{0},H^{1}) }[/math] is called a bihypergraph with the set of 0-edges [math]\displaystyle{ \,E(H^{0}) }[/math] and the set of 1-edges [math]\displaystyle{ \,E(H^{1}) }[/math]. Every hyperedge of either [math]\displaystyle{ \,H^{0} }[/math] or [math]\displaystyle{ \,H^{1} }[/math] is considered as a hyperedge of [math]\displaystyle{ \,H }[/math]. The order of [math]\displaystyle{ \,H }[/math] is [math]\displaystyle{ \,n(H) = |V| }[/math]. The rank of [math]\displaystyle{ \,H }[/math] is [math]\displaystyle{ \,r(H) = \max\{r(H^{0}), r(H^{1})\} }[/math].
A bihypergraph [math]\displaystyle{ \,H = (H^{0}, H^{1}) }[/math] is called bipartite if there exists an ordered partition [math]\displaystyle{ V^{0} \cup V^{1} = V(H) }[/math] (bipartition) such that the set [math]\displaystyle{ \,V^{i} }[/math] is stable in [math]\displaystyle{ \,H^{i} }[/math], [math]\displaystyle{ \,i = 0,1 }[/math].
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.