Stable set
Encyclopedia
The term stable set may refer to:
- The independent setIndependent set (graph theory)In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent. That is, it is a set I of vertices such that for every two vertices in I, there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in I...
in graph theoryGraph theoryIn mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, the set of vertices of a graph not directly connected by edges. - The stable setStable manifoldIn mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor...
in dynamical systems, the set of points leading up to an attractorAttractorAn attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed...
. - The stable set (also known as the Von Neumann-Morgenstern solution) in cooperative gameCooperative gameIn game theory, a cooperative game is a game where groups of players may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players...
s: a set of alternatives satisfying the internal and external stability conditions.