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- W3196911155 abstract "We present an isomorphism test for graphs of Euler genus g running in time 2^{{O}(g⁴ log g)}n^{{O}(1)}. Our algorithm provides the first explicit upper bound on the dependence on g for an fpt isomorphism test parameterized by the Euler genus of the input graphs. The only previous fpt algorithm runs in time f(g)n for some function f (Kawarabayashi 2015). Actually, our algorithm even works when the input graphs only exclude K_{3,h} as a minor. For such graphs, no fpt isomorphism test was known before.The algorithm builds on an elegant combination of simple group-theoretic, combinatorial, and graph-theoretic approaches. In particular, we introduce (t,k)-WL-bounded graphs which provide a powerful tool to combine group-theoretic techniques with the standard Weisfeiler-Leman algorithm. This concept may be of independent interest." @default.
- W3196911155 created "2021-09-13" @default.
- W3196911155 creator A5008306814 @default.
- W3196911155 date "2021-09-01" @default.
- W3196911155 modified "2023-09-23" @default.
- W3196911155 title "Isomorphism Testing Parameterized by Genus and Beyond" @default.
- W3196911155 doi "https://doi.org/10.4230/lipics.esa.2021.72" @default.
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