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,...,2s), where s>=1 is an integer. In this paper, we show that every supereulerian K"1","s-free graph (s>=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.