Lifts, derandomization, and diameters of Schreier graphs of Mealy automata

Abstract

It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and present a class of automata for which the same is true. However, we also show that some automata in this class do not give rise to expander graphs.

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Correspondence to Igor Pak.

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Malyshev, A., Pak, I. Lifts, derandomization, and diameters of Schreier graphs of Mealy automata. Combinatorica 37, 733–765 (2017). https://doi.org/10.1007/s00493-016-3306-0

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Mathematics Subject Classification (2000)

  • 05C25
  • 20F10
  • 68Q70
  • 68R15