  Best match graphs (BMGs) are vertex-colored digraphs that naturally arise in
mathematical phylogenetics to formalize the notion of evolutionary closest
genes w.r.t. an a priori unknown phylogenetic tree. BMGs are explained by
unique least resolved trees. We prove that the property of a rooted,
leaf-colored tree to be least resolved for some BMG is preserved by the
contraction of inner edges. For the special case of two-colored BMGs, this
leads to a characterization of the least resolved trees (LRTs) of
binary-explainable trees and a simple, polynomial-time algorithm for the
minimum cardinality completion of the arc set of a BMG to reach a BMG that can
be explained by a binary tree.
