BACHOC, Christine; NEBE, Gabriele; FILHO, Fernando Mario De Oliveira; VALLENTIN, Frank

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

BACHOC, Christine
Institut de Mathématiques de Bordeaux [IMB]

NEBE, Gabriele

FILHO, Fernando Mario De Oliveira

Idioma

Article de revue

Este ítem está publicado en

Geometric And Functional Analysis. 2009, vol. 19, p. 645-661

Springer Verlag

Resumen en inglés

The Lovasz theta function provides a lower bound for the chromatic number of finite graphs based on the solution of a semidefinite program. In this paper we generalize it so that it gives a lower bound for the measurable chromatic number of distance graphs on compact metric spaces. In particular we consider distance graphs on the unit sphere. There we transform the original infinite semidefinite program into an infinite linear program which then turns out to be an extremal question about Jacobi polynomials which we solve explicitly in the limit. As an application we derive new lower bounds for the measurable chromatic number of the Euclidean space in dimensions 10,..., 24, and we give a new proof that it grows exponentially with the dimension.< Leer menos

Metadatos

Compartir este ítem

Licencia de uso del documento

Lower bounds for measurable chromatic numbers

Idioma

Este ítem está publicado en

Resumen en inglés

URI

Orígen

Centros de investigación