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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| Published in: | Random structures & algorithms Vol. 55; no. 4; pp. 854 - 864 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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New York
John Wiley & Sons, Inc
01.12.2019
Wiley Subscription Services, Inc |
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| ISSN: | 1042-9832, 1098-2418 |
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| 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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| AbstractList | 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. 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. |
| Author | Montgomery, Richard Parczyk, Olaf Han, Jie Böttcher, Julia Person, Yury Kohayakawa, Yoshiharu |
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| Cites_doi | 10.1016/j.aim.2019.106793 10.1002/rsa.20885 10.1112/plms/s3-2.1.69 10.37236/7671 10.1137/15M1032910 10.1016/j.endm.2017.06.033 10.1002/1097-0118(200103)36:3<121::AID-JGT1000>3.0.CO;2-U 10.1017/S0963548316000079 10.37236/278 10.1017/S0963548301004849 10.1002/rsa.10070 10.1007/s00493-007-2182-z 10.1002/9781118032718 10.1016/0012-365X(76)90068-6 10.1007/BF02579198 |
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| SubjectTerms | Apexes Containment Graph theory Graphs perturbed graphs random graphs spanning trees Trees (mathematics) universality |
| Title | Universality for bounded degree spanning trees in randomly perturbed graphs |
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