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A note on the Erdős-Hajnal property for stable graphs


Authors: Artem Chernikov and Sergei Starchenko
Journal: Proc. Amer. Math. Soc. 146 (2018), 785-790
MSC (2010): Primary 03C45, 05C35, 05C69
DOI: https://doi.org/10.1090/proc/13626
Published electronically: October 25, 2017
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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
Email: Starchenko.1@nd.edu

DOI: https://doi.org/10.1090/proc/13626
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
Article copyright: © Copyright 2017 American Mathematical Society

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