The Cover Time of a Biased Random Walk on a Random Cubic Graph

Authors Colin Cooper, Alan Frieze, Tony Johansson

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Author Details

Colin Cooper
  • Department of Informatics, King’s College, University of London, London WC2R 2LS, UK
Alan Frieze
  • Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA 15213, USA
Tony Johansson
  • Department of Mathematics, Uppsala University, 751 05 Uppsala, Sweden

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Colin Cooper, Alan Frieze, and Tony Johansson. The Cover Time of a Biased Random Walk on a Random Cubic Graph. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We study a random walk that prefers to use unvisited edges in the context of random cubic graphs, i.e., graphs chosen uniformly at random from the set of 3-regular graphs. We establish asymptotically correct estimates for the vertex and edge cover times, these being n log n and 3/2 n log n respectively.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Random walk
  • random regular graph
  • cover time


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