Abstract
To a graph G is canonically associated its neighborhood-hypergraph, N( G), formed by the closed neighborhoods of the vertices of G. We characterize the graphs G such that (i) N( G) has no induced cycle, or (ii) N( G) is a balanced hypergraph or (iii) N( G) is triangle free. (i) is another short proof of a result by Farber; (ii) answers a problem asked by C. Berge. The case of strict neighborhoods is also solved.
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