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.