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Journal Article
Matching Numbers and Dimension of Edge Ideals
2021
Overview
Let
G
be a finite simple graph on the vertex set
V
(
G
)
=
{
x
1
,
…
,
x
n
}
and match(
G
), min-match(
G
) and ind-match(
G
) the matching number, minimum matching number and induced matching number of
G
, respectively. Let
K
[
V
(
G
)
]
=
K
[
x
1
,
…
,
x
n
]
denote the polynomial ring over a field
K
and
I
(
G
)
⊂
K
[
V
(
G
)
]
the edge ideal of
G
. The relationship between these graph-theoretic invariants and ring-theoretic invariants of the quotient ring
K
[
V
(
G
)]/
I
(
G
) has been studied. In the present paper, we study the relationship between match(
G
), min-match(
G
), ind-match(
G
) and
dim
K
[
V
(
G
)
]
/
I
(
G
)
.
Publisher
Springer Japan,Springer Nature B.V
Subject
