Vertex-deleted subgraphs and regular factors from regular graph

Let kk, mm, and rr be three integers such that 2≤k≤m≤r2≤k≤m≤r. Let GG be a 2r2r-regular, 2m2m-edge-connected graph of odd order. We obtain some sufficient conditions for G−vG−v to contain a kk-factor for all v∈V(G)v∈V(G).