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