STABILITY INDEX OF DEPTH FUNCTIONSOF COVER IDEALS OF BIPARTITEGRAPHS

Abstract

Let
G
= (
V
(
G
)
, E
(
G
)) be a bipartite graph over the vertex
set
V
(
G
) =
{
1
, . . . , r
}
and
J
(
G
) be the cover ideal of
G
in the polynomial ring
R
=
K
[
x
1
, . . . , x
r
]. In this paper, we give a good bound for the index of
depth stability of
J
(
G
)