A recursive Lovász theta number for simplex-avoiding sets
Davi Castro-Silv (Centrum Wiskunde & Informatica (CWI))
F.M. Filho (TU Delft - Discrete Mathematics and Optimization)
Lucas Slot (Centrum Wiskunde & Informatica (CWI))
Frank Vallentin (University of Cologne, TU Delft - Discrete Mathematics and Optimization)
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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.