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Given a set of triples of a base set $S$, find a subset of triples such that each element in $S$ appears exactly in one triple. This problem is NP-complete by reduction from NP-complete problem 3D Matching.

I'm interested in the complexity of related problem. What is the complexity of finding a subset of triples such that each element in $S$ appears exactly in two triples?

Has this problem been studied in the literature? I'd greatly appreciate pointing me to references.

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  • $\begingroup$ The problem seems to admit a fairly straightforward reduction from 3D matching. $\endgroup$
    – Colin McQuillan
    Commented Apr 24, 2011 at 17:11
  • $\begingroup$ Which reduction do you have in mind for NP-hardness? $\endgroup$
    – Mohammad Al-Turkistany
    Commented Apr 24, 2011 at 18:25

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