Minimum degree, independence number and pseudo [2,b]-factors in graphs

A pseudo [2, b]-factor of a graph G is a spanning subgraph in which each component C on at least three vertices verifies 2 ≤ dC(x) ≤ b, for every vertex x in C. The main contibution of this paper, is to give an upper bound to the number of components that are edges or vertices in a pseudo [2, b]-factor of a graph G. Given an integer b ≥ 4, we show that a graph G with minimum degree δ, independence number α > b(δ−1) 2 and without isolated vertices possesses a pseudo [2, b]-factor with at most α−⌊ b 2 (δ− 1)⌋ edges or vertices. This bound is sharp.