Thickness (graph theory)
Imagine you have a big piece of paper with lots of dots on it. You can see lines that connect some dots to others, right? In graph theory, we call these dots "vertices" and the lines "edges".
Now, let's say you want to color in the edges to show how many things can go through them at the same time. That's where "thickness" comes in.
Thickness means how many colors you need to color in the edges without any two edges of the same color touching each other at the same vertex.
Think of it like painting a fence with different colors. You want to paint each board a different color but you don't want two boards of the same color to touch each other. That's what thickness is in graph theory.
So, the thickness of a graph is the smallest number of colors you need to color in the edges so that no two edges of the same color touch at any vertex.
Now, let's say you want to color in the edges to show how many things can go through them at the same time. That's where "thickness" comes in.
Thickness means how many colors you need to color in the edges without any two edges of the same color touching each other at the same vertex.
Think of it like painting a fence with different colors. You want to paint each board a different color but you don't want two boards of the same color to touch each other. That's what thickness is in graph theory.
So, the thickness of a graph is the smallest number of colors you need to color in the edges so that no two edges of the same color touch at any vertex.