A note on Rees algebras and the MFMC property
Commutative Algebra
2011-04-05 v2 Combinatorics
Abstract
We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an "effective" method, based on the program "Normaliz", to determine whether a given clutter satisfies the max-flow min-cut property. Let C be a clutter and let I be its edge ideal. We prove that C has the max-flow min-cut property if and only if I is normally torsion free, that is, I^i=I^{(i)} for all i>=1, where I^{(i)} is the ith symbolic power of I.
Cite
@article{arxiv.math/0511307,
title = {A note on Rees algebras and the MFMC property},
author = {I. Gitler and C. E. Valencia and R. H. Villarreal},
journal= {arXiv preprint arXiv:math/0511307},
year = {2011}
}
Comments
Beitrage Algebra Geom., to appear