Depth of the 3-path Ideal of Square of a Path

2025/07/11 by Yang, Liuqing, Chu, Lizhong
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.08516

Abstract

In this note, we compute depth of the 3-path ideal of square of a path and show that the 3-path ideal I3(P 2 n) of square of a path graph is Cohen-Macaulay if and only if n = 3 or 4. Also, we consider the limit behavior of depth of powers of the 3-path ideal of square of a path.

Citations

• Depth of powers of edge ideals of Cohen-Macaulay trees
• Depth of powers of edge ideals of cycles and trees
• Depth and Stanley depth of powers of the path ideal of a cycle graph
• Depth and Stanley depth of powers of the path ideal of a path graph
• Edge ideals of squares of trees
• On Chordal Graph and Line Graph Squares
• On the resolution of path ideals of cycles
• Graded Betti numbers of path ideals of cycles and lines
• Uniqueness of graph square roots of girth six
• Depths of Powers of the Edge Ideal of a Tree
• Cohen-Macaulay chordal graphs

Related

• Depth and Stanley depth of powers of the path ideal of a path graph
• Depth and Stanley depth of powers of the path ideal of a cycle graph. II
• Stanley depth of powers of the path ideal
• Depth and Stanley depth of powers of the path ideal of a cycle graph
• Depth and Stanley depth of the path ideal associated to an n-cyclic graph