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The authors give a short proof of a theorem of Lipton and Tarjan, that, for every planar graph with n 0 vertives, there is a partition (A, B, C,) of its vertex set such that $|A|, |B| A is adjacent to any vertex in B. Secondly, they apply the same technique more carefully to deduced that, in fact, such a partition (A, B, C) exists with $|A|, |B|