Equistable graph: различия между версиями
Glk (обсуждение | вклад) (Новая страница: «'''Equistable graph''' --- эквиустойчивый граф. A graph <math>G = (V,E)</math> is '''equistable''' if there is a non-negative weight function <ma…») |
AlexM (обсуждение | вклад) (добавил </math> в конце для закрытия формулы) |
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| Строка 11: | Строка 11: | ||
each constant <math>c \leq 1</math>, there is a non-negative weight function <math>w</math> | each constant <math>c \leq 1</math>, there is a non-negative weight function <math>w</math> | ||
on <math>V</math> such that <math>w(S) = 1</math> for each maximal stable set <math>S</math>, and <math>w(T) | on <math>V</math> such that <math>w(S) = 1</math> for each maximal stable set <math>S</math>, and <math>w(T) | ||
\neq c. | \neq c. </math> | ||
Текущая версия от 18:42, 19 марта 2012
Equistable graph --- эквиустойчивый граф.
A graph [math]\displaystyle{ G = (V,E) }[/math] is equistable if there is a non-negative weight function [math]\displaystyle{ w }[/math] on [math]\displaystyle{ V }[/math] such that a set [math]\displaystyle{ S \subseteq V }[/math] satisfies [math]\displaystyle{ w(S) = \sum_{v \in S} w(e) = 1 }[/math] if and only if [math]\displaystyle{ S }[/math] is maximal stable. The problem of recognizing equistable graphs in polynomial time is still open.
A graph [math]\displaystyle{ G }[/math] is strongly equistable if for each set [math]\displaystyle{ \emptyset \neq T \subseteq V }[/math] such that [math]\displaystyle{ T }[/math] is not maximal stable, and for each constant [math]\displaystyle{ c \leq 1 }[/math], there is a non-negative weight function [math]\displaystyle{ w }[/math] on [math]\displaystyle{ V }[/math] such that [math]\displaystyle{ w(S) = 1 }[/math] for each maximal stable set [math]\displaystyle{ S }[/math], and [math]\displaystyle{ w(T) \neq c. }[/math]