Independent set (graph theory)

Okay kiddo, let's talk about a game called "Friend or Foe". In this game, we have a bunch of friends who each want to be each other's friend, but they also have their own personal space bubble that they don't want to invade.

Now, let's imagine that each friend is a point on a graph and the lines connecting them represent if they are friends or not. If two friends are connected by a line, it means they are friends, and if they aren't connected, they aren't friends.

An independent set is a group of friends who aren't connected to each other. They might know each other, but they decide not to be in each other's personal space bubble. This is like saying they have their own separate group of friends, and they aren't in the same "clique".

So, just like in the "Friend or Foe" game, we can have an independent set where each friend in the set doesn't have any other friends in the set. This is like saying they have their own group of friends and they don't want to be bothered by anyone else.

In graph theory, we use independent sets to study relationships between groups of points or objects, and they can help us understand how those things are related or not related to each other.

So, an independent set is basically a group of friends who have their own space and don't want to invade each other's personal bubbles.