Universality for bounded degree spanning trees in randomly perturbed graphs

We solve a problem of Krivelevich, Kwan and Sudakov concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph Gα on n vertices with δ(Gα) ≥ αn for α > 0 and we add...

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Bibliographic Details
Published in:Random structures & algorithms Vol. 55; no. 4; pp. 854 - 864
Main Authors: Böttcher, Julia, Han, Jie, Kohayakawa, Yoshiharu, Montgomery, Richard, Parczyk, Olaf, Person, Yury
Format: Journal Article
Language:English
Published: New York John Wiley & Sons, Inc 01.12.2019
Wiley Subscription Services, Inc
Subjects:
Apexes
Containment
Graph theory
Graphs
perturbed graphs
random graphs
spanning trees
Trees (mathematics)
universality
ISSN:1042-9832, 1098-2418
Online Access:Get full text
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Summary:We solve a problem of Krivelevich, Kwan and Sudakov concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph Gα on n vertices with δ(Gα) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph Gα∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ.
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20850