List coloring

Hello there! Do you know how to color a picture with crayons or markers? It's really fun, right?

Well, imagine that you have a big list of numbers, like 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. These numbers are called vertices.

Now, let's say we want to color these vertices using only three different colors, let's say red, blue, and green. But we have some rules we need to follow.

The rules say that if two vertices are next to each other (they share an edge), they cannot be the same color. For example, if 1 is red, then 2 and 10 cannot be red.

So, how do we color these vertices? We need to make sure that no two adjacent vertices have the same color. And we can use only red, blue, and green.

One way to do it is to start with the first vertex and color it red. Then we move on to the next vertex and try to color it blue. If it can be blue without breaking the rules, we color it blue. If not, we try green. If neither blue nor green work, we need to change the color of the first vertex and try again.

We keep doing this until we have colored all vertices without any two adjacent vertices having the same color.

This is called list coloring. It's like coloring a picture, but with numbers and rules! It's used in math and computer science to solve problems and puzzles.