On the trace of random walks on random graphs

被引：1

作者：

Frieze, Alan ^{[1
]}

Krivelevich, Michael ^{[2
]}

Michaeli, Peleg ^{[2
]}

Peled, Ron ^{[2
]}

机构：

[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

[2] Tel Aviv Univ, Sch Math Sci, Raymond & Beverly Sackler Fac Exact Sci, IL-6997801 Tel Aviv, Israel

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2018年 / 116卷

基金：

以色列科学基金会;

关键词：

COVER TIME;

D O I：

10.1112/plms.12083

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any epsilon>0 there exists C>1 such that the trace of the simple random walk of length (1+epsilon)nlnn on the random graph G approximate to G(n,p) for p>Clnn/n is, with high probability, Hamiltonian and (lnn)-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.

引用

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页码：847 / 877

页数：31

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