3 research outputs found
Regularity of symbolic powers of edge ideals of unicyclic graphs
Let be a unicyclic graph with edge ideal . For any integer , we denote the -th symbolic power of by . It is shown
that , for every
On the depth of symbolic powers of edge ideals of graphs
Assume that is a graph with edge ideal and star packing number
. We denote the -th symbolic power of by .
It is shown that the inequality is true for every chordal graph and every integer . Moreover, it is proved that for any graph , we have
Upper bounds for the regularity of symbolic powers of certain classes of edge ideals
Let be a finite simple graph and denote the corresponding edge
ideal in a polynomial ring over a field . In this paper, we obtain
upper bounds for the Castelnuovo-Mumford regularity of symbolic powers of
certain classes of edge ideals. We also prove that for several classes of
graphs, the regularity of symbolic powers of their edge ideals coincides with
that of their ordinary powers.Comment: 13 pages, 1 figur