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If the partial order of a set has at most one minimal element, then to test whether it has a non-crossing Hasse diagram its time complexity __________

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If the partial order of a set has at most one minimal element, then to test whether it has a non-crossing Hasse diagram its time complexity __________

(a) NP-complete

(b) O(n^2)

(c) O(n+2)

(d) O(n^3)

This question was addressed to me in an international level competition.

This key question is from Graphs topic in chapter Graphs of Discrete Mathematics

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Best answer
Right choice is (a) NP-complete

Easy explanation: If the partial order has at most one minimal element, or it has at most one maximal element, then to test whether a partial order with multiple sources and sinks can be drawn as a crossing-free Hasse diagram or not it’s time complexity is NP-complete.

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