A collection of LCA constraints is realizable by some DAG if and only if it is realized by the canonical DAG built from the plus-closure of the constraints; the same holds for a regular phylogenetic network.
Theoret- ical Computer Science 363(1):60–68, DOI 10.1016/j.tcs.2006.06.022, computing and Combinatorics
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Inferring DAGs and Phylogenetic Networks from Least Common Ancestors
A collection of LCA constraints is realizable by some DAG if and only if it is realized by the canonical DAG built from the plus-closure of the constraints; the same holds for a regular phylogenetic network.