# Is every planar graph without triangles 3-colorable?

In other words, can a planar graph without k3 have a chromatic number larger than 3?

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Yes, every triangle-free planar graph is 3-colorable. This is known as Grötzsch's theorem.

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It is perhaps worth noting that the theorem does not generalize in the natural way, as evidenced in answers to this question: math.stackexchange.com/questions/225872/… –  Austin Mohr Nov 1 '12 at 2:58