2.9 Coloring & Connectivity

Chromatic Number

1. A graph with maximum degree $$k$$ must have a chromatic number $$\geq k$$.

Exercise 1
Consider the $$n$$-vertex star graph. The central vertex has degree $$n-1$$ but the graph is still 2-colorable.
2. What is the chromatic number for a Wheel graph with $$n$$ vertices, where $$n$$ is even?

Exercise 2
3. How many colors do you need to color a complete graph with $$n$$ vertices?

Exercise 3