TITLE:
Binding Number and Fractional k-Factors of Graphs
AUTHORS:
Renying Chang
KEYWORDS:
Binding Number, Fractional k-Factor, Fractional Matching, Independent Set, Covering Set
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.7,
July
29,
2024
ABSTRACT: In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as
bind(
G
)=min{
|
N
G
(
X
) |
| X |
:∅≠X⊆V(
G
) }
. It is proved that a graph G has a fractional 1-factor if
bind(
G
)≥1
and has a fractional k-factor if
bind(
G
)≥k−
1
k
. Furthermore, it is showed that both results are best possible in some sense.