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Published in:
2007 | OriginalPaper | Chapter
Isolated Toughness and Existence of f-Factors
Authors : Yinghong Ma, Qinglin Yu
Published in: Discrete Geometry, Combinatorics and Graph Theory
Publisher: Springer Berlin Heidelberg
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Let
G
be a graph with vertex set
V
(
G
) and edge set
E
(
G
). The
isolated toughness
of
G
is defined as
I
(
G
) =
min
{|
S
|/
i
(
G
−
S
) |
S
⊆
V
(
G
),
i
(
G
−
S
) ≥ 2} if
G
is not complete; otherwise, set
I
(
G
) = |
V
(
G
)| − 1. Let
f
and
g
be two nonnegative integer-valued functions defined on
V
(
G
) satisfying
a
≤
g
(
x
) ≤
f
(
x
) ≤
b
. The purpose in this paper are to present sufficient conditions in terms of the isolated toughness and the minimum degree for graphs to have
f
-factors and (
g
,
f
)-factors (
g
<
f
). If
g
(
x
) ≡
a
<
b
≡
f
(
x
), the conditions can be weakened.