Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs

2025/09/10 by Trương Thị Hiên, Jiaxin Li, Hien, Truong Thi +5
Computer Science · Mathematics · #05E40 #13C05 #13C15 #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13C14 #Secondary 05C25

paper · pdf · doi:10.48550/arxiv.2509.08677

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the edge ideal I(\D) of a weighted oriented graph \D, we prove that its symbolic powers I(\D)^(t) are Cohen-Macaulay for all t\geqslant 1 if and only if the underlying graph G is composed of a disjoint union of some complete graphs. We also completely characterize the Cohen-Macaulayness of the ordinary powers I(\D)^t for all t\geqslant 2. Furthermore, we provide a criterion for determining whether I(\D)^t=I(\D)^(t).

Citations

• Cohen-Macaulayness of large powers of Stanley-Reisner ideals
• Locally complete intersection Stanley-Reisner ideals
• On the radical of a monomial ideal

Related

• Edge ideals of oriented graphs
• Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs
• Combinatorial characterizations of the Cohen-Macaulayness of the second\n power of edge ideals
• Ordinary and symbolic powers of edge ideals of weighted oriented graphs
• Cohen-Macaulay Weighted Oriented Edge Ideals and its Alexander Dual