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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Vydáno v:Random structures & algorithms Ročník 55; číslo 4; s. 854 - 864
Hlavní autoři: Böttcher, Julia, Han, Jie, Kohayakawa, Yoshiharu, Montgomery, Richard, Parczyk, Olaf, Person, Yury
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York John Wiley & Sons, Inc 01.12.2019
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Témata:
Apexes
Containment
Graph theory
Graphs
perturbed graphs
random graphs
spanning trees
Trees (mathematics)
universality
ISSN:1042-9832, 1098-2418
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20850