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Pseudorandom hypergraph matchings

Part of: Graph theory Extremal combinatorics

Published online by Cambridge University Press:  22 July 2020

Stefan Ehard ,
Stefan Glock  and
Felix Joos
Stefan Ehard
Affiliation:
Institut für Optimierung und Operations Research, Universität Ulm, Germany
Stefan Glock*
Affiliation:
Institute for Theoretical Studies, ETH Zürich, Switzerland
Felix Joos
Affiliation:
Institut für Informatik, Universität Heidelberg, Germany
*
*Corresponding author. Email: stefan.glock@eth-its.ethz.ch
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Abstract

A celebrated theorem of Pippenger states that any almost regular hypergraph with small codegrees has an almost perfect matching. We show that one can find such an almost perfect matching which is ‘pseudorandom’, meaning that, for instance, the matching contains as many edges from a given set of edges as predicted by a heuristic argument.

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs 05C65: Hypergraphs 05C70: Factorization, matching, partitioning, covering and packing
Secondary: 05D15: Transversal (matching) theory 05D40: Probabilistic methods
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 6 , November 2020 , pp. 868 - 885
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

†

The research leading to these results was partially supported by the EPSRC, grants EP/N019504/1 (S. Glock) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 339933727 (F. Joos).

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