**Computational Complexity**

It is possible to determine in polynomial time whether a given finite partially ordered set has order dimension at most two, for instance, by testing whether the comparability graph of the partial order is a permutation graph. However, for any *k* ≥ 3, it is NP-complete to test whether the order dimension is at most *k* (Yannakakis 1982).

Read more about this topic: Order Dimension

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