Bibliographic Details
| Title: |
On the trace of random walks on random graphs. |
| Authors: |
Frieze, Alan, Krivelevich, Michael, Michaeli, Peleg, Peled, Ron |
| Superior Title: |
Proceedings of the London Mathematical Society; Apr2018, Vol. 116 Issue 4, p1-877, 31p |
| Subject Terms: |
RANDOM walks, RANDOM graphs, PROBABILITY theory, HAMILTONIAN systems, NATURAL numbers |
| Abstract: |
We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any ε > 0 there exists C > 1 such that the trace of the simple random walk of length (1 + ε)n ln n on the random graph G~G(n, p) for p > C ln n/n is, with high probability, Hamiltonian and Θ(ln n)-connected. In the special case p = 1 (that is, when G = Kn), 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |
