# Dividing planar graph into two acycliс

Is it true that for any planar graph $(V,E)$ we can divide its set of vertices $V$ into two subsets $V=V_1\sqcup V_2$ such that subgraphs with these sets of vertices (and all edges between them) are both acyclic?

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As you probably realize, this is a strengthening of the four colorability of planar graphs, so you should expect/hope to find a counterexample. – user83827 Dec 10 '11 at 22:26