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On a property of neighborhood hypergraphs

Konrad Pióro (2006)

Commentationes Mathematicae Universitatis Carolinae

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 𝒢 and a hypergraph have the same neighborhood hypergraph and the neighborhood relation in 𝒢 is a subrelation of such a relation in , then is inscribed into 𝒢 (both seen as coverings). In particular, if is also a clique hypergraph, then = 𝒢 .

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