Graph Triangulations and the Compatibility of Unrooted Phylogenetic Trees

TL;DR

This paper links the compatibility of unrooted phylogenetic trees to the existence of a specific triangulation in a derived graph, providing a new graph-theoretic criterion for phylogenetic compatibility.

Contribution

It introduces the concept of legal triangulations of display graphs to characterize the compatibility of unrooted phylogenetic trees, extending triangulation-based methods.

Findings

Legal triangulations characterize tree compatibility

Provides a graph-theoretic criterion for phylogenetic analysis

Extends known triangulation methods to unrooted trees

Abstract

We characterize the compatibility of a collection of unrooted phylogenetic trees as a question of determining whether a graph derived from these trees --- the display graph --- has a specific kind of triangulation, which we call legal. Our result is a counterpart to the well known triangulation-based characterization of the compatibility of undirected multi-state characters.