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Associativity and non-associativity of some hypergraph products

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arxiv 1511.07162 v1 pith:QDMKOFZA submitted 2015-11-23 math.CO

Richard H. Hammack , Marc Hellmuth , Lydia Ostermeier , Peter F. Stadler This is my paper · ORCID
classification math.CO
keywords productdirectproductshypergraphpreservingranksomestrong
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Several variants of hypergraph products have been introduced as generalizations of the strong and direct products of graphs. Here we show that only some of them are associative. In addition to the Cartesian product, these are the minimal rank preserving direct product, and the normal product. Counter-examples are given for the strong product as well as the non-rank-preserving and the maximal rank preserving direct product.

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