Logarithmic Weisfeiler-Leman Identifies All Planar Graphs

  title={Logarithmic Weisfeiler-Leman Identifies All Planar Graphs},
  author={Martin Grohe and Sandra Kiefer},
The Weisfeiler-Leman (WL) algorithm is a well-known combinatorial procedure for detecting symmetries in graphs and it is widely used in graph-isomorphism tests. It proceeds by iteratively refining a colouring of vertex tuples. The number of iterations needed to obtain the final output is crucial for the parallelisability of the algorithm. We show that there is a constant k such that every planar graph can be identified (that is, distinguished from every non-isomorphic graph) by the k… 

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