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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the Erdős-Hajnal property for stable graphs
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by Artem Chernikov and Sergei Starchenko PDF
Proc. Amer. Math. Soc. 146 (2018), 785-790 Request permission

Abstract:

In this note we give a proof of the Erdős–Hajnal conjecture for families of finite (hyper-)graphs without the $m$-order property. This theorem is in fact implicitly proved by M. Malliaris and S. Shelah (2014), however we use a new technique of independent interest combining local stability and pseudo-finite model theory.
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Additional Information
  • Artem Chernikov
  • Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
  • Email: chernikov@math.ucla.edu
  • Sergei Starchenko
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 237161
  • Email: Starchenko.1@nd.edu
  • Received by editor(s): December 10, 2016
  • Published electronically: October 25, 2017
  • Additional Notes: The first author was partially supported by ValCoMo (ANR-13-BS01-0006), by the Fondation Sciences Mathematiques de Paris (FSMP) and by the Investissements d’avenir program (ANR-10-LABX-0098)
    The second author was partially supported by the NSF Research Grant DMS-1500671
  • Communicated by: Mirna Džamonja
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 785-790
  • MSC (2010): Primary 03C45, 05C35, 05C69
  • DOI: https://doi.org/10.1090/proc/13626
  • MathSciNet review: 3731711