The number of cutvertices in graphs with given minimum degree (Q912123)

Let h(n,d) denote the maximum number of cutvertices in a connected graph of order n having minimum degree at least d. The authors show that for \(n-1d>\geq 5\), \[ h(n,d)=2\lfloor \frac{n}{d+1}\rfloor +2\lfloor \frac{n}{(d+1)(d^ 2-2)}\rfloor +e(n), \] where e(n) is well-defined and \(\epsilon\) \(\{\)-3,-2,-1,0\(\}\).