Hamiltonicity via cohomology of right-angled Artin groups

TL;DR

This paper links the Hamiltonian property of a graph to the cohomology algebra of its associated right-angled Artin group, introducing a new canonical graph related to matrix determinants.

Contribution

It establishes a novel characterization of graph Hamiltonicity through cohomology algebra and introduces a new canonical graph construction for matrices.

Findings

Hamiltonicity characterized by cohomology algebra structure

Introduction of a new canonical graph associated with matrices

Provides a new perspective on matrix determinants

Abstract

Let $\Gamma$ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. We characterize the Hamiltonicity of $\Gamma$ via the structure of the cohomology algebra of $A(\Gamma)$. In doing so, we define and develop a new canonical graph associated to a matrix, which as a consequence provides a novel perspective on the matrix determinant.