A recursive Lov\'asz theta number for simplex-avoiding sets
Combinatorics
2022-05-25 v2 Metric Geometry
Abstract
We recursively extend the Lov\'asz 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 -simplex is exponentially Ramsey, and we improve existing bounds for the base of the exponential.
Keywords
Cite
@article{arxiv.2106.09360,
title = {A recursive Lov\'asz theta number for simplex-avoiding sets},
author = {Davi Castro-Silva and Fernando Mário de Oliveira Filho and Lucas Slot and Frank Vallentin},
journal= {arXiv preprint arXiv:2106.09360},
year = {2022}
}
Comments
(v2) 14 pages, 3 figures, background information on Euclidean Ramsey theory added