Four Color Converse
Probability
Level
1
The four color theorem states that all planar graphs have chromatic number at most four. The converse statement is an easier problem to approach: are all graphs with chromatic number at most four planar?
No.
Yes.
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Consider the bipartite non planar graph K(3,3). Since it is bipartite, it can be colored with only two colors, although it is non planar (Kuratowski's Theorem).