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We know that minimal edge cover for the normal graph is polynomial time solvable. Is it also true for hypergraph?

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The polynomial algorithm for "classical" graph is based on a maximum matching algorithm completed with the isolated nodes. 3-dimensional matching is known to be NP-complete (https://en.wikipedia.org/wiki/3-dimensional_matching). This is a case of minimal edge cover for hypergraph. Thus the answer is no.

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  • $\begingroup$ My actual question is I have sets each of cardinality 3.I want to find set cover.How can I solve it? $\endgroup$ – Manoharsinh Rana Jan 31 at 12:08
  • $\begingroup$ in a tripartite graph or not necessary ? $\endgroup$ – Vince Jan 31 at 12:42
  • $\begingroup$ I am talking about this. en.wikipedia.org/wiki/Set_cover_problem only difference is that each set has exactly three element. What I am doing is that treat each set as an edge, each element as a vertex.That will create hypergraph.Now I want to find edge cover of this hypergraph. Is it polynomial time? $\endgroup$ – Manoharsinh Rana Jan 31 at 13:20
  • $\begingroup$ No it is not polynomial, only cardinality 2 is. $\endgroup$ – Vince Jan 31 at 13:39
  • $\begingroup$ is the maximal matching of hypergraph polynomial time solvable? $\endgroup$ – Manoharsinh Rana Jan 31 at 14:48

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