Circuit

Circuit — цикл.

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.