Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals

Abstract

Let (P,<) be a finite poset and let G be its comparability graph. If cl(G) is the clutter of maximal cliques of G, we prove that cl(G) satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. We prove that edge ideals of complete admissible uniform clutters are normally torsion free. The normality of a monomial ideal is expressed in terms of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property completely determine their normality