Subgraphs of minimal degree k

For k ? 2, any graph G with n vertices and (k?1)(n?k+2)+(2k?2) edges has a subrgraph of minimum degree at least k; however, this subgraph need not be proper. It is shown that if G has at least (k?1)(n?k+2)+(2k?2)+1 edges, then there is a subgraph H of minimal degree k that has at most n ? ?n;?6k3vertices. Also, conditions that insure the existense of smaller subgraphs of minimum degree k are given.