Total Ordering Problem Total Ordering Problem
Paper summary Proves the NP-completeness of the total ordering problem: given finite sets $S$ and $R$, where $R$ is a subset of $S \times S \times S$, 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 \cite{garey1979computers}.

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