Affiliation:
1. Department of Mathematics, Qinghai Nationalities University , Xining , Qinghai 810000 , People’s Republic of China
Abstract
Abstract
A connected even
[
2
,
2
s
]
{[}2,2s]
-factor of a graph G is a connected factor with all vertices of degree
i
(
i
=
2
,
4
,
…
,
2
s
)
i(i=2,4,\ldots ,2s)
, where
s
≥
1
s\ge 1
is an integer. In this paper, we show that a
k
+
1
s
+
2
\tfrac{k+1}{s+2}
-tough k-tree has a connected even
[
2
,
2
s
]
{[}2,2s]
-factor and thereby generalize the result that a
k
+
1
3
\tfrac{k+1}{3}
-tough k-tree is Hamiltonian in [Hajo Broersma, Liming Xiong, and Kiyoshi Yoshimoto, Toughness and hamiltonicity in k-trees, Discrete Math. 307 (2007), 832–838].
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