# Connected to relation

Перейти к:навигация, поиск

Connected to relationотношение связности ''к'', (достижимость) в гиперграфе.

The relation connected to, which is denoted by the symbol $\succ$, is defined for a given subset $\,R$ of nodes and a node $\,y$; we say that $\,R$ is connected to $\,y$ and write $R \succ y$ if and only if a directed hyperpath exsists in a hypergraph from $\,R$ to the node $\,y$.

It is easy to check that the relation $\succ$ satisfies the following set of connectivity axioms:

(1) $y \in R \subseteq V \Rightarrow R \succ y$ (reflexivity);

(2) $R \succ y\mbox{ and } Z \subseteq V \Rightarrow (R \cup Z) \succ y$ (augmentation);

(3) $R \succ y, \; \forall y \in Y,\mbox{ and }Y \succ z \Rightarrow R \succ z$ (transitivity).

## Литература

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