Hey guys, I tried to find a solution to this in the web but couldn't. Can you tell me if the following sentence is correct or else give me a counterexample? G is 4-colorable iff each sub-graph G' in G is not isomorphic to K5. At first glance it seems to be related to the four color theorem but it is not exactly a planar graph (e.g. 3x3 complete bipartite graph) so it is not identical to FCT. Any ideas?

Thanks!