Monomial ideals of weighted oriented graphs
Yuriko Pitones, Enrique Reyes, Jonathan Toledo
TL;DR
This paper investigates the algebraic properties of edge ideals derived from weighted oriented graphs, providing decompositions, prime characterizations, and conditions for Cohen-Macaulayness, with specific focus on bipartite, whisker, and cycle graphs.
Contribution
It offers a comprehensive combinatorial and algebraic analysis of the edge ideal I(D), including irredundant decompositions, prime characterizations, and Cohen-Macaulay conditions for various graph classes.
Findings
Irreducible decomposition of I(D) determined
Characterization of associated primes and unmixed property provided
Conditions for Cohen-Macaulay property established
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.
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