Abstract
A connected even [ 2 , 2 s ] -factor of a graph G is a connected factor with all vertices of degree i ( i = 2 , 4 , … , 2 s ), 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 , 2 s - 2 ] -factor, hereby generalizing the result that every 4-connected claw-free graph has a connected [ 2 , 4 ] -factor by Broersma, Kriesell and Ryjacek.
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