Hamiltonicity via cohomology of right-angled Artin groups.

Let Γ be a finite graph and let A (Γ) be the corresponding right-angled Artin group. We characterize the Hamiltonicity of Γ via the structure of the cohomology algebra of A (Γ). 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. [ABSTRACT FROM AUTHOR]