Grün's lemma
Okay, so have you ever played with a jigsaw puzzle? You know how all the pieces have to fit perfectly together in order to complete the picture? Well, mathematicians have their own kind of puzzle called a graph. It's made up of little dots (called vertices) and lines (called edges) that connect them.
Now, Grün's Lemma is a rule that we can use when we have a special kind of graph called a planar graph. That means a graph that we can draw on a flat surface and none of the edges will cross over each other. Just like how we can draw a map of a neighborhood on a piece of paper without having any roads overlap.
Grün's Lemma tells us that if we have a planar graph with a certain number of vertices and edges, then we can color it with just two colors without any of the edges that touch each other having the same color. It's kind of like how you might color in a coloring book - you don't want two areas that touch each other to be the same color.
So, in summary, Grün's Lemma helps us color a special kind of puzzle called a planar graph with just two colors without any of the edges that touch each other having the same color.
Now, Grün's Lemma is a rule that we can use when we have a special kind of graph called a planar graph. That means a graph that we can draw on a flat surface and none of the edges will cross over each other. Just like how we can draw a map of a neighborhood on a piece of paper without having any roads overlap.
Grün's Lemma tells us that if we have a planar graph with a certain number of vertices and edges, then we can color it with just two colors without any of the edges that touch each other having the same color. It's kind of like how you might color in a coloring book - you don't want two areas that touch each other to be the same color.
So, in summary, Grün's Lemma helps us color a special kind of puzzle called a planar graph with just two colors without any of the edges that touch each other having the same color.