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Random perturbation of sparse graphs
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Published in: | The electronic journal of combinatorics pages:1-12; volume:28; elocationid:#P2.26; year:2021; 28(2021), 2, Artikel-ID #P2.26, Seite 1-12; number:2 |
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Authors and Corporations: | , , , , , , |
Other Authors: | Maesaka, Giulia Satiko [Author] • Mogge, Yannick [Author] • Mohr, Samuel 1992- [Author] • Parczyk, Olaf 1988- [Author] |
Type of Resource: | E-Book Component Part |
Language: | English |
published: |
2021
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Series: |
The electronic journal of combinatorics, 28(2021), 2, Artikel-ID #P2.26, Seite 1-12
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Source: | Verbunddaten SWB Lizenzfreie Online-Ressourcen |
ISSN: | 1077-8926 |
License: |
Summary: | In the model of randomly perturbed graphs we consider the union of a deterministic graph G with minimum degree αn and the binomial random graph 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 Pósa and Korshunov on the threshold in G(n, p). In this note we extend this result in G ∪G(n, p) to sparser graphs with α = o(1). More precisely, for any ε > 0 and α: N ↦→ (0, 1) we show that a.a.s. G ∪ G(n, β/n) is Hamiltonian, where β = −(6 + ε) log(α). If α > 0 is a fixed constant this gives the aforementioned result by Bohman, Frieze, and Martin and if α = O(1/n) the random part G(n, p) is sufficient for a Hamilton cycle. We also discuss embeddings of bounded degree trees and other spanning structures in this model, which lead to interesting questions on almost spanning embeddings into G(n, p). α α α |
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Item Description: |
Sonstige Körperschaft: Technische Universität Hamburg Sonstige Körperschaft: Technische Universität Hamburg, Institut für Mathematik |
ISSN: | 1077-8926 |
DOI: | 10.15480/882.3578 |
Access: | Open Access |