We prove that every triconnected planar graph on n vertices is definable by a first order sentence that uses at most 15 variables and has quantifier depth at most 11 log_2 n + 45. As a consequence, a canonic form of such graphs is computable in AC~1 by the 14-dimensional Weisfeiler-Lehman algorithm. This gives us another AC~1 algorithm for the planar graph isomorphism.
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机译：我们证明，在n个顶点上的每个三连通平面图都可以由使用最多15个变量并且量化器深度最多为11 log_2 n + 45的一阶句子来定义。因此，此类图的规范形式可以在AC〜中计算出来。由14维Weisfeiler-Lehman算法得出。这为平面图同构提供了另一种AC〜1算法。
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