On the depth of binomial edge ideals of graphs

Let G be a graph on the vertex set [ n ] and J G the associated binomial edge ideal in the polynomial ring S = K [ x 1 , … , x n , y 1 , … , y n ] . In this paper, we investigate the depth of binomial edge ideals. More precisely, we first establish a combinatorial lower bound for the depth of S / J...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2022-05, Vol.55 (3), p.827-846
Main Authors: Rouzbahani Malayeri, M., Saeedi Madani, S., Kiani, D.
Format: Article
Language:English
Subjects:
Combinatorial analysis
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Homology
Lattices
Lower bounds
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Polynomials
Rings (mathematics)
Set theory
Vertex sets
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Summary:Let G be a graph on the vertex set [ n ] and J G the associated binomial edge ideal in the polynomial ring S = K [ x 1 , … , x n , y 1 , … , y n ] . In this paper, we investigate the depth of binomial edge ideals. More precisely, we first establish a combinatorial lower bound for the depth of S / J G based on some graphical invariants of G . Next, we combinatorially characterize all binomial edge ideals J G with depth S / J G = 5 . To achieve this goal, we associate a new poset M G with the binomial edge ideal of G and then elaborate some topological properties of certain subposets of M G in order to compute some local cohomology modules of S / J G .
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-021-01072-4