Bridge: различия между версиями
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'''Bridge''' | '''Bridge''' — ''[[мост]].'' | ||
'''1.''' A '''bridge''' of a ''cycle'' <math>C</math> is the shortest path in <math>C</math> joining | '''1.''' A '''bridge''' of a ''[[cycle]]'' <math>C</math> is the shortest [[path]] in <math>C</math> joining | ||
nonconsecutive vertices of <math>C</math> which is shorter than both of the edges | nonconsecutive vertices of <math>C</math> which is shorter than both of the [[edge|edges]] | ||
of <math>C</math> joining those vertices. Thus a ''chord'' is a bridge of | of <math>C</math> joining those [[vertex|vertices]]. Thus a ''[[chord]]'' is a bridge of | ||
length 1, and a graph is bridged iff every cycle of length at least 4 | length 1, and a [[graph, undirected graph, nonoriented graph|graph]] is bridged iff every cycle of length at least 4 | ||
has a bridge. | has a bridge. | ||
'''2.''' A '''bridge''' of <math>G</math> is an edge whose removal disconnects <math>G</math>. | '''2.''' A '''bridge''' of <math>G</math> is an edge whose removal disconnects <math>G</math>. | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 16:31, 23 октября 2018
Bridge — мост.
1. A bridge of a cycle [math]\displaystyle{ C }[/math] is the shortest path in [math]\displaystyle{ C }[/math] joining nonconsecutive vertices of [math]\displaystyle{ C }[/math] which is shorter than both of the edges of [math]\displaystyle{ C }[/math] joining those vertices. Thus a chord is a bridge of length 1, and a graph is bridged iff every cycle of length at least 4 has a bridge.
2. A bridge of [math]\displaystyle{ G }[/math] is an edge whose removal disconnects [math]\displaystyle{ G }[/math].
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.