Exercise 18.

Decide whether the following statements are true or false. Prove your answers.

  1. If two graph \(G_1\) and \(G_2\) have the same chromatic number, then they are isomorphic.

  2. If two graphs \(G_1\) and \(G_2\) have the same number of vertices and edges and have the same chromatic number, then they are isomorphic.

  3. If two graphs are isomorphic, then they have the same chromatic number.

Solution.
in-context