Independence number and [a, b]-factors of graphs

Let G be a graph. The cardinality of any largest independent set of vertices in G is called the independence number of G and is denoted by alpha(G). Let a and b be integers with 0 <= a <= b. If a = b, it is assumed that G be a connected graph, furthermore, a >= alpha(G), a vertical bar V(G)vertical bar 0 (mod 2) if a is odd. We prove that every graph G has an [a, b]-factor if its minimum degree is at least (b+alpha(G)a-alpha(G)/b) [b+alpha(G)a/2 alpha(G)] - alpha(G)/b ([b+alpha(G)a/2 alpha(G)])(2) + theta alpha(G)(2)/b + a/b alpha(G) where theta = 0 if a < b, and theta = 1 if a = b. This degree condition is sharp.