Abstract
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 log2 n + 45. As a consequence, a canonic form of such graphs is computable in AC1 by the 14-dimensional Weisfeiler-Lehman algorithm. This gives us another AC1 algorithm for the planar graph isomorphism. © Springer-Verlag Berlin Heidelberg 2007.
Cite
CITATION STYLE
Verbitsky, O. (2007). Planar graphs: Logical complexity and parallel isomorphism tests. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4393 LNCS, pp. 682–693). Springer Verlag. https://doi.org/10.1007/978-3-540-70918-3_58
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