Bridged graph: различия между версиями
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'''Bridged graph''' | '''Bridged graph''' — ''[[граф с мостами]].'' | ||
A graph <math>G</math> is a '''bridged graph''' if each cycle <math>C</math> of length at least 4 | A [[graph, undirected graph, nonoriented graph|graph]] <math>G</math> is a '''bridged graph''' if each [[cycle]] <math>C</math> of length at least 4 | ||
contains two vertices whose distance from each other in <math>G</math> is | contains two [[vertex|vertices]] whose distance from each other in <math>G</math> is | ||
strictly less than that in <math>C</math>. | strictly less than that in <math>C</math>. | ||
A graph is called '''bridged''' if every cycle of length at least 4 | A graph is called '''bridged''' if every cycle of length at least 4 | ||
has a ''bridge''. Observe that in a bridged graph every cycle of | has a ''bridge''. Observe that in a bridged graph every cycle of | ||
length 4 or 5 has a chord. Bridged graphs are in general not perfect, | length 4 or 5 has a chord. Bridged graphs are in general not perfect, | ||
as the ''wheel'' <math>W_{7}</math> shows. | as the ''[[wheel]]'' <math>W_{7}</math> shows. | ||
==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
Bridged graph — граф с мостами.
A graph [math]\displaystyle{ G }[/math] is a bridged graph if each cycle [math]\displaystyle{ C }[/math] of length at least 4 contains two vertices whose distance from each other in [math]\displaystyle{ G }[/math] is strictly less than that in [math]\displaystyle{ C }[/math]. A graph is called bridged if every cycle of length at least 4 has a bridge. Observe that in a bridged graph every cycle of length 4 or 5 has a chord. Bridged graphs are in general not perfect, as the wheel [math]\displaystyle{ W_{7} }[/math] shows.
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.