English

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

Data Structures and Algorithms 2021-03-12 v1 Discrete Mathematics Combinatorics Populations and Evolution

Abstract

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.

Cite

@article{arxiv.2103.06665,
  title  = {Arc-Completion of 2-Colored Best Match Graphs to Binary-Explainable Best Match Graphs},
  author = {David Schaller and Manuela Geiß and Marc Hellmuth and Peter F. Stadler},
  journal= {arXiv preprint arXiv:2103.06665},
  year   = {2021}
}
R2 v1 2026-06-23T23:59:48.059Z