A reconstruction problem for a class of phylogenetic networks with lateral gene transfers

We introduce a set of simple conditions on an LGT network that guarantee that its principal and secondary phylogenetic subtrees are pairwise different and that these subtrees determine, up to isomorphism, the LGT network. We then give an algorithm that, given a set of pairwise different phylogenetic trees [Formula: see text] on the same set of taxa, outputs, when it exists, the LGT network that satisfies these conditions and such that its principal phylogenetic tree is [Formula: see text] and its secondary phylogenetic trees are [Formula: see text].