A recursive Lovász theta number for simplex-avoiding sets

Journal article (2022)

Authors

Davi Castro-Silv Centrum Wiskunde & Informatica (CWI)
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS
Lucas Slot Centrum Wiskunde & Informatica (CWI)
F. Vallentin Discrete Mathematics and Optimization - EEMCS , University of Cologne
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2022 Davi Castro-Silv, F.M. de Oliveira Filho, Lucas Slot, F. Vallentin
DOI: https://doi.org/10.1090/proc/15940
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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

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-simplex is exponentially Ramsey, and we improve existing bounds for the base of the exponential.

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