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The relation between facets of Rees cones of clutters and irreducible b-vertex covers is examined. Let G be a simple graph and let I c (G) be its ideal of vertex covers. We give a graph theoretical description of the irreducible b-vertex covers of G, i.e., we describe the minimal generators of the symbolic Rees algebra of I c (G). As an application we… (More)

Using the theory of integer programming, we study the canonical module and the a-invariant of certain monomial subrings associated to systems with the integer rounding property. For systems arising from cliques of perfect graphs explicit expressions for the canonical module and the a-invariant are given. It is shown that a system has the integer rounding… (More)

The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial ideals and monomial subrings. We study the normality and Gorenstein property—as well as the canonical module and the a-invariant—of Rees algebras and subrings arising from systems… (More)

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… (More)

- Luis A. Dupont, Rafael H. Villarreal
- J. Comb. Optim.
- 2011

Let C be a uniform clutter and let A be the incidence matrix of C. We denote the column vectors of A by v1,. .. , vq. Under certain conditions we prove that C is vertex critical. If C satisfies the max-flow min-cut property, we prove that A diagonalizes over Z to an identity matrix and that v1,. .. , vq form a Hilbert basis. We also prove that if C has a… (More)

Let C be a uniform clutter and let I = I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C 1 satisfying the packing property (resp. max-flow min-cut property) such that C is a minor of C 1. For arbitrary edge ideals of clutters we prove that the… (More)

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