Sharp threshold for the appearance of certain spanning trees in random graphs

Dan Hefetz; Michael Krivelevich; Tibor Szabó

doi:10.1002/rsa.20472

Sharp threshold for the appearance of certain spanning trees in random graphs

Dan Hefetz^*
, Michael Krivelevich
, Tibor Szabó

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove that a given tree T on n vertices with bounded maximum degree is contained asymptotically almost surely in the binomial random graph G(n, (1+ε) log n/n) provided that T belongs to one of the following two classes: (1) T has linearly many leaves; (2) T has a path of linear length all of whose vertices have degree two in T.

Original language	English
Pages (from-to)	391-412
Number of pages	22
Journal	Random Structures and Algorithms
Volume	41
Issue number	4
DOIs	https://doi.org/10.1002/rsa.20472
State	Published - Dec 2012

Keywords

Random graphs
Sharp thresholds
Spanning trees
Tree-universality

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10.1002/rsa.20472

Cite this

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title = "Sharp threshold for the appearance of certain spanning trees in random graphs",

abstract = "We prove that a given tree T on n vertices with bounded maximum degree is contained asymptotically almost surely in the binomial random graph G(n, (1+ε) log n/n) provided that T belongs to one of the following two classes: (1) T has linearly many leaves; (2) T has a path of linear length all of whose vertices have degree two in T.",

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AU - Krivelevich, Michael

AU - Szabó, Tibor

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AB - We prove that a given tree T on n vertices with bounded maximum degree is contained asymptotically almost surely in the binomial random graph G(n, (1+ε) log n/n) provided that T belongs to one of the following two classes: (1) T has linearly many leaves; (2) T has a path of linear length all of whose vertices have degree two in T.

KW - Random graphs

KW - Sharp thresholds

KW - Spanning trees

KW - Tree-universality

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Sharp threshold for the appearance of certain spanning trees in random graphs

Abstract

Keywords

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