Automorphisms and quotients of 2-colored quasi best match graphs

TL;DR

This paper explores the structural properties and automorphism groups of 2-colored quasi best match graphs, revealing their potential for constructing graphs with large symmetry groups relevant in phylogenetics.

Contribution

It provides new insights into the automorphism groups of 2-qBMGs and methods to construct graphs with large automorphism groups, extending understanding beyond computational issues.

Findings

Undirected underlying graphs lack induced paths and cycles of size ≥6.

Results on automorphism group structures of 2-qBMGs.

Methods to construct 2-qBMGs with large automorphism groups.

Abstract

2-colored quasi best match graphs (2-qBMGs) are directed graphs that arose in phylogenetics. Investigations of 2-qBMGs have mostly focused on computational issues. However, 2-qBMGs also have relevant properties for structural graph theory; in particular, their undirected underlying graph is free from induced paths and cycles of size at least 6. In this paper, results on the structure of the automorphism groups of 2-qBMGs are obtained, which shows how to construct 2-qBMGs with large automorphism groups.