Corpus ID: 237278741

The complexity of testing all properties of planar graphs, and the role of isomorphism

@article{Basu2021TheCO,
  title={The complexity of testing all properties of planar graphs, and the role of isomorphism},
  author={Sabyasachi Basu and Akash Kumar and Seshadhri Comandur},
  journal={Electron. Colloquium Comput. Complex.},
  year={2021},
  volume={28},
  pages={122}
}
Consider property testing on bounded degree graphs and let ε > 0 denote the proximity parameter. A remarkable theorem of Newman-Sohler (SICOMP 2013) asserts that all properties of planar graphs (more generally hyperfinite) are testable with query complexity only depending on ε. Recent advances in testing minor-freeness have proven that all additive and monotone properties of planar graphs can be tested in poly(ε) queries. Some properties falling outside this class, such as Hamiltonicity, also… Expand

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