A Resistance Bound Via An Isoperimetric Inequality

An isoperimetric upper bound on the resistance is given. As a corollary we resolve two problems, regarding mean commute time on finite graphs and resistance on percolation clusters. Further conjectures are presented.

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Correspondence to Itai Benjamini.

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Benjamini, I., Kozma, G. A Resistance Bound Via An Isoperimetric Inequality. Combinatorica 25, 645–650 (2005). https://doi.org/10.1007/s00493-005-0040-4

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Mathematics Subject Classification (2000):

  • 60J45
  • 60C05
  • 60K