The stability number and connected -factor in graphs

Let G be a graph with vertex set V ( G ) . A spanning subgraph F of G is called a [ k , k + 1 ] -factor if k ≤ d F ( x ) ≤ k + 1 for every x ∈ V ( F ) . F is called a connected factor of G if F is connected. In this work we present a sufficient condition for the existence of connected [ k , k + 1 ] -factors in graphs. The condition involves the stability number and degree conditions of graph G .