Аноним

Circuit: различия между версиями

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(Новая страница: «'''Circuit''' --- цикл. '''1.''' The same as ''Cycle''. '''2.''' Given a graph <math>G</math>, a '''circuit''' is a walk <math>(x_{1}, e_{1}, \ldots, x_{k}, e…»)
 
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'''Circuit''' --- цикл.  
'''Circuit''' — ''[[цикл]].''


'''1.''' The same as ''Cycle''.
'''1.''' The same as ''[[Cycle]]''.


'''2.''' Given a graph <math>G</math>, a '''circuit''' is a walk <math>(x_{1}, e_{1}, \ldots, x_{k}, e_{k},
'''2.''' Given a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math>, a '''circuit''' is a walk <math>(x_{1}, e_{1}, \ldots, x_{k}, e_{k},
x_{k+1})</math> such that <math>x_{1}, \ldots, x_{k}</math> are distinct vertices,
x_{k+1})</math> such that <math>x_{1}, \ldots, x_{k}</math> are distinct [[vertex|vertices]],
<math>e_{1}, \ldots, e_{k}</math> are distinct edges and <math>x_{1} = x_{k+1}</math>. If
<math>e_{1}, \ldots, e_{k}</math> are distinct [[edge|edges]] and <math>\,x_{1} = x_{k+1}</math>. If
the graph is ''simple'', we will denote it by <math>(x_{1}, \ldots,
the graph is ''[[simple graph|simple]]'', we will denote it by <math>(x_{1}, \ldots,
x_{k})</math>.
x_{k})</math>.


'''3.''' Given a hypergraph, a '''circuit''' is a sequence <math>(x_{1}, E_{1},</math> <math>\ldots,</math> <math>x_{k}</math>,
'''3.''' Given a [[hypergraph]], a '''circuit''' is a sequence <math>(x_{1}, E_{1},\ldots,x_{k}, E_{k})</math>, where <math>x_{1}, \ldots, x_{k}</math> are distinct vertices, <math>E_{1},
<math>E_{k})</math>, where <math>x_{1}, \ldots, x_{k}</math> are distinct vertices, <math>E_{1},
\ldots, E_{k}</math> are distinct edges and <math>x_{i} \in E_{i}</math>, <math>i = 1,
\ldots, E_{k}</math> are distinct edges and <math>x_{i} \in E_{i}</math>, <math>i = 1,
\ldots, k</math>, <math>x_{i+1} \in E_{i}</math>, <math>i = 1, \ldots, k-1</math>, and <math>x_{1} \in
\ldots, k</math>, <math>x_{i+1} \in E_{i}</math>, <math>i = 1, \ldots, k-1</math>, and <math>x_{1} \in
E_{k}</math>. Here <math>k</math> is the length of this circuit.
E_{k}</math>. Here <math>\,k</math> is the length of this circuit.
 
==Литература==
 
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.