A connected even
[2,2s]-factor of a graph
G is a connected factor with all vertices of degree
i (
i=2,4,…,2s), where
s1 is an integer. In this paper, we show that every supereulerian
K1,s-free graph
(s2) contains a connected even
[2,2s-2]-factor, hereby generalizing the result that every 4-connected claw-free graph has a connected
[2,4]-factor by Broersma, Kriesell and Ryjacek.