I've just learned about the four color theorem. So my question is: "Given an undirected graph if I am able to color this undirected graph with 1,2,3 or at most colors 4 colors such that no two vertices with the same colors are adjacent, can I by the four color theorem conclude that the graph is a planar graph"?
Using the four color theorem to check if a graph is Planar
graph theory
Best Answer
The four-colour theorem only stats that if a graph is planar then it can be coloured by at most four colours. It does not state the converse, and indeed $K_{3,3}$ is bipartite – can be coloured with only two colours – but is not planar.