The stability number and connected [k,k+1][k,k+1]-factor in graphs

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