skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Krivelevich, M"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; (, Journal of the London Mathematical Society)
    We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any $$\varepsilon>0$$ there exists $C>1$ such that the trace of the simple random walk of length $$(1+\varepsilon)n\ln{n}$$ on the random graph $$G\sim\gnp$$ for $$p>C\ln{n}/n$$ is, with high probability, Hamiltonian and $$\Theta(\ln{n})$$-connected. In the special case $p=1$$ (i.e.\ when $$G=K_n$), we show a hitting time result according to which, with high probability, exactly one step after the last vertex has been visited, the trace becomes Hamiltonian, and one step after the last vertex has been visited for the $$k$$'th time, the trace becomes $2k$-connected. 
    more » « less
    Accepted Manuscript Full Text Available