Hamiltonicity via cohomology of right-angled Artin groups

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.

arXiv comment14 pages. To appear in Linear Algebra and its Applications