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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• SODA
• 2021
• 1
• PDF

#### References

SHOWING 1-10 OF 26 REFERENCES
Embedding spanning bounded degree subgraphs in randomly perturbed graphs
• Mathematics, Computer Science
• Electron. Notes Discret. Math.
• 2017
• 16
• PDF
Spanning universality in random graphs
• Mathematics, Computer Science
• Random Struct. Algorithms
• 2018
• 10
• PDF
Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs
• Mathematics, Computer Science
• Random Struct. Algorithms
• 2019
• 16
• PDF
Embedding Spanning Trees in Random Graphs
• 49
• PDF
Universality for bounded degree spanning trees in randomly perturbed graphs
• Computer Science, Mathematics
• Random Struct. Algorithms
• 2019
• 28
• PDF
Bounded-Degree Spanning Trees in Randomly Perturbed Graphs
• Mathematics, Computer Science
• SIAM J. Discret. Math.
• 2017
• 37
• PDF
On Pósa's Conjecture for Random Graphs
• Mathematics, Computer Science
• SIAM J. Discret. Math.
• 2012
• 36
• PDF
Spanning Subgraphs of Random Graphs
• O. Riordan
• Mathematics, Computer Science
• Combinatorics, Probability and Computing
• 2000
• 48