Abstract
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.
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