Regularity of powers of edge ideals: from local properties to global bounds

An upper bound for the regularity of powers of edge ideals

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$‎, ‎denoted by match$(G)$‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph $G$ and every $sgeq 1$‎, ‎$${rm reg}( R‎/ ‎I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...

Regularity of second power of edge ideals

Let G be a graph with edge ideal I(G). Benerjee and Nevo proved that for every graph G, the inequality reg(I(G)2)≤reg(I(G))+2 holds. We provide an alternative proof for this result.

Regularity Bounds for Binomial Edge Ideals

We show that the Castelnuovo–Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.

LINEAR RESOLUTIONS of POWERS of EDGE IDEALS

We discuss the linearity of the minimal free resolution of a power of an edge ideal.

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs