Irredundance perfect graph: различия между версиями
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A graph <math>G</math> is '''minimal irredundance imperfect''' if <math>G</math> is not | A graph <math>G</math> is '''minimal irredundance imperfect''' if <math>G</math> is not | ||
irredundance perfect and <math>ir(H) = \gamma(H)</math> for every proper | |||
induced subgraph <math>H</math> of <math>G</math>. | induced subgraph <math>H</math> of <math>G</math>. | ||
Текущая версия от 14:41, 24 мая 2011
Irredundance perfect graph --- неизбыточно совершенный граф.
A graph [math]\displaystyle{ G }[/math] is an irredundance perfect graph, if for every induced subgraph [math]\displaystyle{ H }[/math] of [math]\displaystyle{ G }[/math] holds the equality [math]\displaystyle{ ir(H) = \gamma(H) }[/math], where [math]\displaystyle{ ir(H) }[/math] is the irredundance number and [math]\displaystyle{ \gamma(H) }[/math] is the domination number. A graph [math]\displaystyle{ G }[/math] is called [math]\displaystyle{ k }[/math]-irredundance perfect ([math]\displaystyle{ k \geq 1 }[/math]) if [math]\displaystyle{ ir(H) = \gamma(H) }[/math] for every induced subgraph [math]\displaystyle{ H }[/math] of [math]\displaystyle{ G }[/math] with [math]\displaystyle{ ir(H) \leq k }[/math].
A graph [math]\displaystyle{ G }[/math] is minimal irredundance imperfect if [math]\displaystyle{ G }[/math] is not irredundance perfect and [math]\displaystyle{ ir(H) = \gamma(H) }[/math] for every proper induced subgraph [math]\displaystyle{ H }[/math] of [math]\displaystyle{ G }[/math].
The first sufficient condition, for a graph to be irredundance perfect, in terms of a family of forbidden induced subgraphs is due to Bollob\'{a}s and Cockayne (1979).