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

Abstract

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let G be the comparability graph of a finite poset. 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. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.