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- W3162138899 abstract "We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width." @default.
- W3162138899 created "2021-05-24" @default.
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- W3162138899 date "2021-04-26" @default.
- W3162138899 modified "2023-10-02" @default.
- W3162138899 title "Isomorphism, canonization, and definability for graphs of bounded rank width" @default.
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- W3162138899 doi "https://doi.org/10.1145/3453943" @default.
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