Stable Set

A stable set, also known as an independent set, is a group of vertices in a graph where no two vertices are directly connected by an edge. In other words, within this set, no pair of elements has a relationship or link between them. Stable sets are useful in scenarios like scheduling, where tasks or events in the same set do not overlap or conflict. Finding the largest stable set helps identify the maximum number of items that can coexist without direct interaction or interference, and it’s a fundamental concept in graph theory with applications across computer science, operations research, and network design.