arXiv:2402.16166v1 [math.AC] 25 Feb 2024 Page 1 arXiv:2402.16166v1 [math.AC] 25 Feb 2024
PROJECTIVE DIMENSION AND REGULARITY OF 3-PATH IDEALS OF UNICYCLIC GRAPHS …

We provide formulas for the projective dimension and the regularity of edge ideals
associated to vertex weighted rooted forests and oriented cycles. We derive from that exact …

Let I be the t-path ideal of Ln, the line graph with n-vertices. It is shown that Is has a linear
resolution for some s≥ 1 (or equivalently for all s≥ 1) if and only if Is has linear quotients for …

Let $ S= K [x_1,\ldots, x_n] $ and let $ I $ be the $ t $-path ideal of the line graph $ L_n $ with
$ n $-vertices. It is shown that the set of associated prime ideals of $ I^ s $ is equal to the set …

Let G be a simple graph and I 3 (G) be its 3-path ideal in the corresponding polynomial ring
R. In this article, we prove that for an arbitrary graph G, reg (R/I 3 (G)) is bounded below by 2 …

In this article, we study the linearity of the minimal free resolution of powers of facets ideals
of simplicial trees. We give a complete characterization of simplicial trees for which (some) …

Projective Dimension and Regularity of Powers of Edge Ideals of Vertex-Weighted Rooted
Forests | SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a …

Let D be a weighted oriented graph with the underlying graph G and I (D), I (G) be the edge
ideals corresponding to D and G respectively. We show that the regularity of edge ideal of a …

In this article, we give combinatorial formulas for the regularity and the projective dimension
of $3 $-path ideals of chordal graphs, extending the well-known formulas for the edge ideals …

In this paper we provide some exact formulas for the projective dimension and the regularity
of edge ideals of vertex-weighted oriented unicyclic graphs. These formulas are in function …