Total ordering problem

{{Summary
 * title=Total Ordering Problem
 * authors=J. Opatrný
 * tags=complexity, np-complete, computational complexity
 * summary=Proves the NP-completeness of the total ordering problem: given finite sets S and R, where R is a subset of S x S x S, does there exist a total ordering of the elements of S such that for all (x, y, z) in R, either x < y < z or z < y < x? The reduction is from the hypergraph 2-colorability problem with edges of size at most 3.

This problem is in "Computers and Intractibility" by Garey and Johnson as problem MS1, the betweenness problem.