A recursive Lovász theta number for simplex-avoiding sets-Reference-Cited by-同舟云学术

A recursive Lovász theta number for simplex-avoiding sets

Published:2022-04-01 Issue:8 Volume:150 Page:3307-3322
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Castro-Silva Davi,de Oliveira Filho Fernando,Slot Lucas,Vallentin Frank

Abstract

We recursively extend the Lovász theta number to geometric hypergraphs on the unit sphere and on Euclidean space, obtaining an upper bound for the independence ratio of these hypergraphs. As an application we reprove a result in Euclidean Ramsey theory in the measurable setting, namely that every k k -simplex is exponentially Ramsey, and we improve existing bounds for the base of the exponential.

Funder

Horizon 2020 Framework Programme

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2022-150-08/S0002-9939-2022-15940-1/proc15940_AM.pdf

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