A De Bruijn-Erdős theorem for $1$-$2$ metric spaces

Title:

A De Bruijn-Erdős theorem for $1$-$2$ metric spaces

Creator:

Chvátal, Vašek

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:24be29ac-3087-407d-9f6b-12c06b4e0956
uuid:24be29ac-3087-407d-9f6b-12c06b4e0956

Subject:

line in metric space and De Bruijn-Erd\H os theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chvátal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces where each nonzero distance equals $1$ or $2$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

45-51

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:1

Harvested from:

CDK

Metadata only:

false