We give an isomorphism test that runs in time $n^{\operatorname{polylog}(h)}$ on all $n$-vertex graphs excluding some $h$-vertex vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016) and $n^{f(h)}$ for some function $f$ (Grohe and Marx, SIAM J. Comp., 2015). Our result also unifies and extends previous isomorphism tests for graphs of maximum degree $d$ running in time $n^{\operatorname{polylog}(d)}$ (FOCS 2018) and for graphs of Hadwiger number $h$ running in time $n^{\operatorname{polylog}(h)}$ (FOCS 2020).

翻译：我们给出一个按时间运行的异形测试, 运行时间为 $ ⁇ operatorname{polylog}(h)}, 运行时间为 $@operatorname{polylog}(n)}(Babai, STOC 2016) 和 $ ⁇ f(h)}$, 运行时间为 $f$(Grohe和Marx, SIAM J.comp., 2015) 。我们的结果还统一并扩展了以前对以时间运行时间为 $ ⁇ operatorname{polylog}(d)}(FOCS 2018) 和以时间运行的Hadwiger number $h$(h) 运行时间为 $ ⁇ operatorname{polylog}(h) 的异形测试(FOCS 2020) 。