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

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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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Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA

    Anton Malyshev & Igor Pak

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  1. Anton Malyshev
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  2. Igor Pak
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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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  • DOI: https://doi.org/10.1007/s00493-016-3306-0

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