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3-dimensional matching : ウィキペディア英語版 | 3-dimensional matching
In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (a.k.a. 2-dimensional matching) to 3-uniform hypergraphs. Finding a largest 3-dimensional matching is a well-known NP-hard problem in computational complexity theory. ==Definition==
Let ''X'', ''Y'', and ''Z'' be finite, disjoint sets, and let ''T'' be a subset of ''X'' × ''Y'' × ''Z''. That is, ''T'' consists of triples (''x'', ''y'', ''z'') such that ''x'' ∈ ''X'', ''y'' ∈ ''Y'', and ''z'' ∈ ''Z''. Now ''M'' ⊆ ''T'' is a 3-dimensional matching if the following holds: for any two distinct triples (''x''1, ''y''1, ''z''1) ∈ ''M'' and (''x''2, ''y''2, ''z''2) ∈ ''M'', we have ''x''1 ≠''x''2, ''y''1 ≠''y''2, and ''z''1 ≠''z''2.
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