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The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree

Author Tony Johansson

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  • 14 pages

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Author Details

Tony Johansson
  • Department of Mathematics, Uppsala University, Uppsala, Sweden

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Tony Johansson. The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 45:1-45:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


We consider a random walk process, introduced by Orenshtein and Shinkar [Tal Orenshtein and Igor Shinkar, 2014], which prefers to visit previously unvisited edges, on the random r-regular graph G_r for any odd r >= 3. We show that this random walk process has asymptotic vertex and edge cover times 1/(r-2)n log n and r/(2(r-2))n log n, respectively, generalizing the result from [Cooper et al., to appear] from r = 3 to any larger odd r. This completes the study of the vertex cover time for fixed r >= 3, with [Petra Berenbrink et al., 2015] having previously shown that G_r has vertex cover time asymptotic to rn/2 when r >= 4 is even.

Subject Classification

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


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