Connected even factors in claw-free graphs

A connected even $[2,2s]$-factor of a graph $G$ is a connected factor with all vertices of degree $i(i=2,4,\ldots,2s)$, where $s\ge 1$ is an integer. In this paper, we show that every supereulerian $K_{1,s}$-free graph $(s\ge 2)$ 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.