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- W3037697850 abstract "The Colour Refinement procedure and its generalisation to higher dimensions, the Weisfeiler-Leman algorithm, are central subroutines in approaches to the graph isomorphism problem. In an iterative fashion, Colour Refinement computes a colouring of the vertices of its input graph. A trivial upper bound on the iteration number of Colour Refinement on graphs of order n is n-1. We show that this bound is tight. More precisely, we prove via explicit constructions that there are infinitely many graphs G on which Colour Refinement takes |G|-1 iterations to stabilise. Modifying the infinite families that we present, we show that for every natural number n ≥ 10, there are graphs on n vertices on which Colour Refinement requires at least n-2 iterations to reach stabilisation." @default.
- W3037697850 created "2020-07-02" @default.
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- W3037697850 date "2020-01-01" @default.
- W3037697850 modified "2023-10-09" @default.
- W3037697850 title "The Iteration Number of Colour Refinement" @default.
- W3037697850 doi "https://doi.org/10.4230/lipics.icalp.2020.73" @default.
- W3037697850 hasPublicationYear "2020" @default.
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