The structure of 2-colored best match graphs

Recent investigations in computational biology have focused on a family of 2-colored digraphs, called best match graphs (briefly 2-BMGs), which naturally arise from rooted phylogenetic trees. Actually the defining properties 2-BMG are unusual apart bi-transitivity, and natural question is whether 2-BMGs also well fit structural graph theory. In this paper we show some such properties. A major result that if has no equivalent vertices then each its orientation acyclic. We point out arising topological ordering can efficiently be used for enumeration reconstruction smaller almost 2-BMGs.