Random graph matching at Otter's threshold via counting chandeliers

@article{Mao2022RandomGM,
  title={Random graph matching at Otter's threshold via counting chandeliers},
  author={Cheng Mao and Yihong Wu and Jiaming Xu and Sophie H. Yu},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.12313}
}
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erdős–Rényi graphs G(n, q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nq →∞ and the edge correlation coefficient ρ satisfies ρ > α ≈ 0.338, where α is Otter’s tree-counting… 

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