Loose ear decompositions and their applications to right-angled Artin groups

TL;DR

This paper explores the relationship between graph theory and right-angled Artin groups (RAAGs) by characterizing graph properties through RAAGs and introducing loose ear decompositions to analyze their structure.

Contribution

It introduces loose ear decompositions of RAAGs and characterizes graph properties like planarity and minors using these decompositions, extending classical graph concepts.

Findings

Characterization of planar graphs via RAAGs

Identification of graph minors through RAAGs

Development of loose ear decompositions for RAAGs

Abstract

We characterize planar graphs and graph minors among other graph theoretic notions in terms of right-angled Artin groups (RAAGs). For this, we determine all sets of elements in RAAGs with ears as underlying graphs that are exactly the sets of vertex generators. Generalizing ear decompositions of graphs to loose ear decompositions, we characterize both decompositions in terms of RAAGs. The desired results follow as applications of loose ear decompositions of RAAGs.