On the Stanley depth of edge ideals of line and cyclic graphs

Abstract

We prove that the edge ideals of line and cyclic graphs and their quotient rings satisfy the Stanley conjecture. We compute the Stanley depth for the quotient ring of the edge ideal associated to a cycle graph of length $n$, given a precise formula for $n\equiv 0,2(\mathrm{mod}3)$ and tight bounds for $n\equiv 1(\mathrm{mod}3)$. Also, we give bounds for the Stanley depth of a quotient of two monomial ideals, in combinatorial terms.

8 pages. Will appear in Romanian Journal of Mathematics and Computer Science

References in corpus (2)

• A non-partitionable Cohen-Macaulay simplicial complex
• Stanley depth of powers of the path ideal

Cited by in corpus (2)

• Regularity and $a$-invariant of Cameron--Walker graphs
• Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph