Monomial ideals of weighted oriented graphs

Abstract

Let I=I(D) be the edge ideal of a weighted oriented graph D. We determine the irredundant irreducible decomposition of I. Also, we characterize the associated primes and the unmixed property of I. Furthermore, we give a combinatorial characterization for the unmixed property of I, when D is bipartite, D is a whisker or D is a cycle. Finally, we study the Cohen-Macaulay property of I.

15 pages

Cited by in corpus (4)

• Comparing symbolic powers of edge ideals of weighted oriented graphs
• Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals
• Barile-Macchia resolutions
• Normally torsion-free edge ideals of weighted oriented graphs