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