Hyperfinite graphings and combinatorial optimization

Abstract

We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorial optimization. We show how invariance of hyperfiniteness of graphings under local isomorphism can be reformulated as an infinite version of a natural combinatorial optimization problem, and how one can prove it by extending wellknown proof techniques (linear relaxation, greedy algorithm, linear programming duality) from the finite case to the infinite.

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Correspondence to L. Lovász.

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Dedicated to Endre Szemerédi at the occasion of his 80th birthday

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Lovász, L. Hyperfinite graphings and combinatorial optimization. Acta Math. Hungar. (2020). https://doi.org/10.1007/s10474-020-01065-y

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Key words and phrases

  • hyperfinite
  • splitting set
  • greedy algorithm

Mathematics Subject Classification

  • primary 05C72
  • secondary 05C63
  • 05C35