# Circuit

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Circuitцикл.

1. The same as Cycle.

2. Given a graph $\,G$, a circuit is a walk $(x_{1}, e_{1}, \ldots, x_{k}, e_{k}, x_{k+1})$ such that $x_{1}, \ldots, x_{k}$ are distinct vertices, $e_{1}, \ldots, e_{k}$ are distinct edges and $\,x_{1} = x_{k+1}$. If the graph is simple, we will denote it by $(x_{1}, \ldots, x_{k})$.

3. Given a hypergraph, a circuit is a sequence $(x_{1}, E_{1},\ldots,x_{k}, E_{k})$, where $x_{1}, \ldots, x_{k}$ are distinct vertices, $E_{1}, \ldots, E_{k}$ are distinct edges and $x_{i} \in E_{i}$, $i = 1, \ldots, k$, $x_{i+1} \in E_{i}$, $i = 1, \ldots, k-1$, and $x_{1} \in E_{k}$. Here $\,k$ is the length of this circuit.

## Литература

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