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

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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 
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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/