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Article
A note on the last new vertex visited by a random walk
Article first published online: 5 OCT 2006
DOI: 10.1002/jgt.3190170505
Copyright © 1993 Wiley Periodicals, Inc., A Wiley Company
1097-0118/asset/cover.gif?v=1&s=747ee645df081de59c78864878c8bdb9daeca9a1 "Journal of Graph Theory")
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How to Cite
Lovász, L. and Winkler, P. (1993), A note on the last new vertex visited by a random walk. J. Graph Theory, 17: 593–596. doi: 10.1002/jgt.3190170505
Publication History
- Issue published online: 5 OCT 2006
- Article first published online: 5 OCT 2006
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Abstract
A “cover tour” of a connected graph G from a vertex x is a random walk that begins at x, moves at each step with equal probability to any neighbor of its current vertex, and ends when it has hit every vertex of G. The cycle Cn is well known to have the curious property that a cover tour from any vertex is equally likely to end at any other vertex; the complete graph Kn shares this property, trivially, by symmetry. Ronald L. Graham has asked whether there are any other graphs with this property; we show that there are not. © 1993 John Wiley & Sons, Inc.