P-Critical graph: различия между версиями
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'''<math>p</math>-Critical graph''' - | '''<math>\,p</math>-Critical graph''' — ''[[p-Критический граф|<math>\,p</math>-критический граф]].'' | ||
A graph <math>G</math> is '''<math>p</math>-critical''' if <math>G</math> is not ''perfect'' but | |||
every proper induced subgraph of <math>G</math> is perfect. The celebrated ''Strong Perfect Graph Conjecture'' (SPGC) of C. Berge states that | A [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> is '''<math>\,p</math>-critical''' if <math>\,G</math> is not ''[[perfect graph|perfect]]'' but every proper [[induced (with vertices) subgraph|induced subgraph]] of <math>\,G</math> is perfect. The celebrated ''[[Strong perfect graph conjecture|Strong Perfect Graph Conjecture]]'' (SPGC) of C. Berge states that <math>\,p</math>-critical graphs are only <math>\,C_{2n+1}</math> and <math>\,C_{2n+1}^{c}</math>, <math>\,n \geq 2</math>. | ||
<math>p</math>-critical graphs are only <math>C_{2n+1}</math> and <math>C_{2n+1}^{c}</math>, <math>n \geq 2</math>. | |||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 04:58, 13 апреля 2018
[math]\displaystyle{ \,p }[/math]-Critical graph — [math]\displaystyle{ \,p }[/math]-критический граф.
A graph [math]\displaystyle{ \,G }[/math] is [math]\displaystyle{ \,p }[/math]-critical if [math]\displaystyle{ \,G }[/math] is not perfect but every proper induced subgraph of [math]\displaystyle{ \,G }[/math] is perfect. The celebrated Strong Perfect Graph Conjecture (SPGC) of C. Berge states that [math]\displaystyle{ \,p }[/math]-critical graphs are only [math]\displaystyle{ \,C_{2n+1} }[/math] and [math]\displaystyle{ \,C_{2n+1}^{c} }[/math], [math]\displaystyle{ \,n \geq 2 }[/math].
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.