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

Author:

Schaller DavidORCID,Geiß ManuelaORCID,Hellmuth MarcORCID,Stadler Peter F.ORCID

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.

Funder

Deutsche Forschungsgemeinschaft

Publisher

MDPI AG

Subject

Computational Mathematics,Computational Theory and Mathematics,Numerical Analysis,Theoretical Computer Science

Reference21 articles.

1. Best match graphs

2. Corrigendum to “Best Match Graphs”;Schaller;J. Math. Biol.,2021

3. The Structure of 2-Colored Best Match Graphs;Korchmaros;arXiv,2020

4. Circles and Paths in 2-Colored Best Match Graphs;Korchmaros;arXiv,2020

5. Generating a Random Sink-free Orientation in Quadratic Time

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1. Best Match Graphs with Binary Trees;IEEE/ACM Transactions on Computational Biology and Bioinformatics;2022

2. Generating the Triangulations of the Torus with the Vertex-Labeled Complete 4-Partite Graph K2,2,2,2;Symmetry;2021-08-03

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