A recursive Lovász theta number for simplex-avoiding sets

Davi Castro-Silv; Fernando Mário De Oliveira Filho; Lucas Slot; Frank Vallentin

doi:10.1090/proc/15940

A recursive Lovász theta number for simplex-avoiding sets

Davi Castro-Silv, Fernando Mário De Oliveira Filho, Lucas Slot, Frank Vallentin

Discrete Mathematics and Optimization

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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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.

Original language	English
Pages (from-to)	3307-3322
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	8
DOIs	https://doi.org/10.1090/proc/15940
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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A recursive Lovász theta number for simplex-avoiding sets

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