On the cover time of the emerging giant

Alan Frieze; Wesley Pegden; Tomasz Tkocz

On the cover time of the emerging giant

Combinatorics 2022-11-23 v4

Authors: Alan Frieze , Wesley Pegden , Tomasz Tkocz

Abstract

Let $p=\frac{1+\varepsilon}{n}$ . It is known that if $N=\varepsilon^3n\to\infty$ then w.h.p. $G_{n,p}$ has a unique giant largest component. We show that if in addition, $\varepsilon=\varepsilon(n)\to 0$ then w.h.p. the cover time of $G_{n,p}$ is asymptotic to $n\log^2N$ ; previously Barlow, Ding, Nachmias and Peres had shown this up to constant multiplicative factors.

Keywords

cover time random graph giant component gnp model asymptotic behavior

Cite

@article{arxiv.1808.09608,
  title  = {On the cover time of the emerging giant},
  author = {Alan Frieze and Wesley Pegden and Tomasz Tkocz},
  journal= {arXiv preprint arXiv:1808.09608},
  year   = {2022}
}

Comments

We fixed an error in the proof

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