Toughness and [a,b]-factors with inclusion/exclusion properties

In this paper, we investigate the existence of [a,b]-factors with inclusion/exclusion properties under the toughness condition. We prove that if an incomplete graph G satisfies t(G) (a-1) + ab and a,b are two integers with b > a > 1, then for any two given edges e1 and e2, there exist an [a,b]-factor including e1,e2; and an [a,b]-factor including e1 and excluding e2; as well as an [a,b]-factor excluding e1,e2 unless e1 and e2 have a common end in the case of a = 2. For complete graphs, we obtain a similar r...