We extend a structural result by A. Dress and M. Steel, "Convex tree realizations of partitions," Applied Math Letters,
5 (1993), pp. 3–6., to show that the three-state
Perfect Phylogeny problem reduces in polynomial time to the classic 2-SAT problem. We also
give a more expanded exposition of the proof of the structural result from Dress and Steel.
We hope this note will encourage additional researchers to try to solve the central open question:
finding simple efficient solutions to the k-state Perfect Phylogeny problem for k > 3.