The Structure of 2-Colored Best Match Graphs

TL;DR

This paper studies the structural properties of 2-colored best match graphs from phylogenetics, proving acyclicity in their underlying bipartite graphs and leveraging topological orderings for graph construction.

Contribution

It establishes that certain underlying bipartite graphs of these structures are acyclic and introduces methods to construct new graphs using topological orderings.

Findings

Underlying bipartite graphs are acyclic.

Topological orderings enable efficient graph construction.

Provides insights connecting biological graphs to structural graph theory.

Abstract

Recent investigations in computational biology have focused on a family of 2-colored digraphs, called 2-colored best match graphs, which naturally arise from rooted phylogenetic trees. Actually the defining properties of such graphs are unusual, and a natural question is whether they also have properties which well fit in structural graph theory. In this paper, we prove that some underlying oriented bipartite graphs of a 2-colored best match graph are acyclic and we point out that the arising topological ordering can efficiently be used for constructing new families of 2-colored best match graphs.