Isomorphism Testing for Graphs Excluding Small Topological Subgraphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866912333139279872 |
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| author | Neuen, Daniel |
| author_facet | Neuen, Daniel |
| contents | 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 $n^{\operatorname{polylog}(d)}$ (SIAM J. Comp., 2023) and for graphs of Hadwiger number $h$ running in time $n^{\operatorname{polylog}(h)}$ (SIAM J. Comp., 2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_14730 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Isomorphism Testing for Graphs Excluding Small Topological Subgraphs Neuen, Daniel Data Structures and Algorithms Discrete Mathematics Combinatorics 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 $n^{\operatorname{polylog}(d)}$ (SIAM J. Comp., 2023) and for graphs of Hadwiger number $h$ running in time $n^{\operatorname{polylog}(h)}$ (SIAM J. Comp., 2023). |
| title | Isomorphism Testing for Graphs Excluding Small Topological Subgraphs |
| topic | Data Structures and Algorithms Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2011.14730 |