Corpus ID: 215548045

Random perturbation of sparse graphs

@article{HahnKlimroth2020RandomPO,
  title={Random perturbation of sparse graphs},
  author={Max Hahn-Klimroth and G. S. Maesaka and Yannick Mogge and S. Mohr and O. Parczyk},
  journal={arXiv: Combinatorics},
  year={2020}
}
In the model of randomly perturbed graphs we consider the union of a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and the binomial random graph $\mathbb{G}(n,p)$. This model was introduced by Bohman, Frieze, and Martin and for Hamilton cycles their result bridges the gap between Dirac's theorem and the results by Posa and Korsunov on the threshold in $\mathbb{G}(n,p)$. In this note we extend this result in $\mathcal{G}_\alpha \cup \mathbb{G}(n,p)$ to sparser graphs… Expand
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