Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-04-30T17:03:30.405Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Conjecture of Bollobás and Brightwell Concerning Random Walks on Product Graphs

Published online by Cambridge University Press:  01 December 1998

OLLE HÄGGSTRÖM
OLLE HÄGGSTRÖM
Affiliation:
Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden (e-mail: olleh@math.chalmers.se)
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider continuous time random walks on a product graph G×H, where G is arbitrary and H consists of two vertices x and y linked by an edge. For any t>0 and any a, b∈V(G), we show that the random walk starting at (a, x) is more likely to have hit (b, x) than (b, y) by time t. This contrasts with the discrete time case and proves a conjecture of Bollobás and Brightwell. We also generalize the result to cases where H is either a complete graph on n vertices or a cycle on n vertices.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 4 , December 1998 , pp. 397 - 401
Copyright
1998 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)