Arc-Completion of 2-Colored Best Match Graphs to Binary-Explainable Best Match Graphs

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 explained by unique least resolved trees. We prove property rooted, leaf-colored tree be for some BMG is preserved contraction inner edges. For special case two-colored BMGs, this leads characterization trees (LRTs) binary-explainable and simple, polynomial-time algorithm minimum cardinality completion arc set reach can binary