A note on the Erdős-Hajnal property for stable graphs-Reference-Cited by-同舟云学术

A note on the Erdős-Hajnal property for stable graphs

Published:2017-10-25 Issue:2 Volume:146 Page:785-790
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chernikov Artem,Starchenko Sergei

Abstract

In this note we give a proof of the Erdős–Hajnal conjecture for families of finite (hyper-)graphs without the m 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2018-146-02/S0002-9939-2017-13626-0/S0002-9939-2017-13626-0.pdf

Reference7 articles.

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3. P. Erdős and A. Hajnal, Ramsey-type theorems, Discrete Applied Mathematics (1989).

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5. On pseudo-finite dimensions;Hrushovski, Ehud;Notre Dame J. Form. Log.,2013

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