Let π = (d1, . . . , dn) be a non-increasing degree sequence with even n. In 1974, Kundu showed that if Dk(π) = (d1 − k, . . . , dn − k) is graphic, then some realization of π has a k-factor. For r ≤ 2, Busch et al. and later Seacrest for r ≤ 4 showed that