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Contractible Edges and Contractible Triangles in a 3-Connected Graph
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Journal Article
Contractible Edges and Contractible Triangles in a 3-Connected Graph
2021
Overview
Let
G
be a 3-connected graph. An edge (a triangle) of
G
is said to be a 3-contractible edge (a 3-contractible triangle) if the contraction of it results in a 3-connected graph. We denote by
E
c
(
G
)
and
T
c
(
G
)
the set of 3-contractible edges of
G
and the set of 3-contractible triangles of
G
, respectively. We prove that if
|
V
(
G
)
|
≥
7
, then
|
E
c
(
G
)
|
+
15
14
|
T
c
(
G
)
|
≥
6
7
|
V
(
G
)
|
.
We also determine the extremal graphs.
Publisher
Springer Science and Business Media LLC,Springer Japan,Springer Nature B.V
