1. A De Bruijn-Erdős theorem for $1$-$2$ metric spaces
- Creator:
- Chvátal, Vašek
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- line in metric space and De Bruijn-Erd\H os theorem
- Language:
- English
- 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 $2$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public