Universality for bounded degree spanning trees in randomly perturbed graphs

Julia Böttcher; Jie Han; Yoshiharu Kohayakawa; Richard Montgomery; Olaf Parczyk; Yury Person

doi:10.1002/rsa.20850

Universality for bounded degree spanning trees in randomly perturbed graphs

Julia Böttcher^*, Jie Han, Yoshiharu Kohayakawa, Richard Montgomery, Olaf Parczyk, Yury Person

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

32 引用（Scopus）

摘要

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 G_α on n vertices with δ(G_α) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph G_α∪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.

源语言	英语
页（从-至）	854-864
页数	11
期刊	Random Structures and Algorithms
卷	55
期	4
DOI	https://doi.org/10.1002/rsa.20850
出版状态	已出版 - 1 12月 2019
已对外发布	是

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title = "Universality for bounded degree spanning trees in randomly perturbed graphs",

abstract = "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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author = "Julia B{\"o}ttcher and Jie Han and Yoshiharu Kohayakawa and Richard Montgomery and Olaf Parczyk and Yury Person",

note = "Publisher Copyright: {\textcopyright} 2019 The Authors. Random Structures and Algorithms published by Wiley Periodicals, Inc.",

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AU - Böttcher, Julia

AU - Han, Jie

AU - Kohayakawa, Yoshiharu

AU - Montgomery, Richard

AU - Parczyk, Olaf

AU - Person, Yury

PY - 2019/12/1

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N2 - 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.

AB - 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.

KW - perturbed graphs

KW - random graphs

KW - spanning trees

KW - universality

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JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 4

ER -

Universality for bounded degree spanning trees in randomly perturbed graphs

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