[a,b]-factorizations of graphs

Let a and b be integers with b ? a ? 0. A graph G is called an a,b]-graph if a ? d_G(v) ? b for each vertex v ∈ V(G), and an a,b]-factor of a graph G is a spanning a,b]-subgraph of G. A graph is a,b]-factorable if its edges can be decomposed into a,b]-factors. The purpose of this paper is to prove the following three theorems: (i) if 1 ? b ? 2a, every (12a + 2)m + 2an,(12b + 4)m + 2bn]-graph is 2a, 2b + 1]-factorable; (ii) if b ? 2a ?1, every (12a ?4)m + 2an, (12b ?2)m + 2bn]-graph is 2a ?1,2b]-factorable; and (iii) if b ? 2a ?1, every (6a ?2)m + 2an, (6b + 2)m + 2bn]-graph is 2a ?1,2b + 1]-factorable, where m and n are nonnegative integers. They generalize some a,b]-factorization results of Akiyama and Kano 3], Kano 6], and Era 5].