TITLE:
2-Factors with a Few Components in Balanced Bipartite Graphs
AUTHORS:
Huanxin Pei
KEYWORDS:
2-Factor, Bipartite Graph, Degree Condition
JOURNAL NAME:
Engineering,
Vol.16 No.11,
November
15,
2024
ABSTRACT: In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n
(
n≥6
)
and
e(
G
)>
n
2
−2n+4
contains a 2-factor with k components,
2
d
1
-cycle,
⋯
,
2
d
k
-cycle, if one of the following is satisfied: (1)
k=2
,
δ(
G
)≥2
and
d
1
−2≥
d
2
≥2
; (2)
k=3
,
δ(
G
)≥
d
3
+2
and
d
1
−2≥
d
2
≥
d
3
≥4
. In particular, this extends one result of Moon and Moser in 1963 under condition (1).