Systems with the integer rounding property in normal monomial subrings

Abstract

Let C be a clutter and let A be its incidence matrix. If the linear system x ≥ 0; x A ≤ 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Rees algebra of the edge ideal of a bipartite graph is Gorenstein if and only if the graph is unmixed.