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I would like to know the standard definition of k-partite hypergraph.

There are two natural generalizations of k-partite graph to k-partite hypergraph: 1. For all edges e, any two vertices in e are not contained in the same part. (All vertices must come from different parts) 2. For all edges e, all vertices in e are not contained in the same part.

I found papers referring to each definition using the same term “k-partite hypergraph”. Here is what I wonder: Which one of those is more frequently used? I would like to refer to the second one in my article. Is it acceptable to call the second definition k-partite hypergraph, or is there another term for the second case?

Thank you.

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  • $\begingroup$ As long as you clarify what you mean by "k-partite hypergraph" (and perhaps clarify that some other references mean something else with it), there is no problem with you usingthat term. $\endgroup$
    – Wojowu
    Commented Sep 14, 2019 at 8:50
  • $\begingroup$ For the second notion, I would say "properly $k$-coloured". $\endgroup$
    – Ilya Bogdanov
    Commented Sep 14, 2019 at 9:33

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