Geodesic
A De Bruijn-Erdős theorem for $1$-$2$ metric spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 45-51.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $2$.
DOI : 10.1007/s10587-014-0081-1
Classification : 05D99, 51G99
Keywords: line in metric space; De Bruijn-Erd\H os theorem 
@article{10_1007_s10587_014_0081_1,
     author = {Chv\'atal, Va\v{s}ek},
     title = {A {De} {Bruijn-Erd\H{o}s} theorem for $1$-$2$ metric spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {45--51},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {2014},
     doi = {10.1007/s10587-014-0081-1},
     mrnumber = {3247442},
     zbl = {06391474},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0081-1/}
}
TY  - JOUR
AU  - Chvátal, Vašek
TI  - A De Bruijn-Erdős theorem for $1$-$2$ metric spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 45
EP  - 51
VL  - 64
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0081-1/
DO  - 10.1007/s10587-014-0081-1
LA  - en
ID  - 10_1007_s10587_014_0081_1
ER  - 
%0 Journal Article
%A Chvátal, Vašek
%T A De Bruijn-Erdős theorem for $1$-$2$ metric spaces
%J Czechoslovak Mathematical Journal
%D 2014
%P 45-51
%V 64
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0081-1/
%R 10.1007/s10587-014-0081-1
%G en
%F 10_1007_s10587_014_0081_1
Chvátal, Vašek. A De Bruijn-Erdős theorem for $1$-$2$ metric spaces. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 45-51. doi : 10.1007/s10587-014-0081-1. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0081-1/

Cité par Sources :