[a,b]‐factorization of a graph

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Abstract
Let a and b be integers such that 0 ⩽ a ⩽ b. Then a graph G is called an [a, b]‐graph if a ⩽ dG(x) ϵ b for every x ϵ V(G), and an [a, b]‐factor of a graph is defined to be its spanning subgraph F such that a ⩽ dF(x) ⩽ b for every vertex x, where dG(x) and dF(x) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a.b]‐factors then we say that the graph is [2a, 2a]‐factorable. We prove the following two theorems: (i) a graph G is [2a, 2b)‐factorable if and only if G is a [2am,2bm]‐graph for some integer m, and (ii) every [8m + 2k, 10m + 2k]‐graph is [1,2]‐factorable.

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