Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs

Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Gorenstein standard algebra. If the graph G is chordal, we give a description–in terms of cliques–of the symbolic Rees algebra of the edge ideal of G. Certain TDI systems of integral matrices are characterized. Applications to max-flow min-cut problems and monomial subrings are presented.