? A graph is four colorable if and only if it is planar.


Is this true, I know that if a graph is planar it is four colorable, but is it true that if a graph is four colorable it must be a planar graph.


(EDIT) The following would have been a better way for me to have ask the question.
What are the requirements for a graph to be planar?
What are the requirements for a graph to be 4 colorable?
Is there a simplification of the intersection of not planar and four colorable?



? A graph is four colorable if and only if it is planar.
A graph is planar if and only if it does not have $K\_5$ or $K\_{3,3}$ as a minor. As Hunter's comment points out, $K\_{3,3}$ is bipartite, ie two-colourable.


