Geodesic
On a property of neighborhood hypergraphs
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 149-154.

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

The aim of the paper is to show that no simple graph has a proper subgraph with the same neighborhood hypergraph. As a simple consequence of this result we infer that if a clique hypergraph $\Cal G$ and a hypergraph $\Cal H$ have the same neighborhood hypergraph and the neighborhood relation in $\Cal G$ is a subrelation of such a relation in $\Cal H$, then $\Cal H$ is inscribed into $\Cal G$ (both seen as coverings). In particular, if $\Cal H$ is also a clique hypergraph, then $\Cal H = \Cal G$.
Classification : 05C65, 05C69, 05C99
Keywords: graph; neighbor; neighborhood hypergraph; clique hypergraph 
@article{CMUC_2006__47_1_a12,
     author = {Pi\'oro, Konrad},
     title = {On a property of neighborhood hypergraphs},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {149--154},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2006},
     mrnumber = {2223974},
     zbl = {1150.05405},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a12/}
}
TY  - JOUR
AU  - Pióro, Konrad
TI  - On a property of neighborhood hypergraphs
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 149
EP  - 154
VL  - 47
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a12/
LA  - en
ID  - CMUC_2006__47_1_a12
ER  - 
%0 Journal Article
%A Pióro, Konrad
%T On a property of neighborhood hypergraphs
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 149-154
%V 47
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a12/
%G en
%F CMUC_2006__47_1_a12
Pióro, Konrad. On a property of neighborhood hypergraphs. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 149-154. http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a12/