On the connectivity of maximal planar graphs

Let d1 ⩾ d2 ⩾ … ⩾ dp be the vertex degrees of a maximal planar graph G. Etourneau has shown that if d1 ⩽ 6 and dp = 5, then G is 5-connected. We generalize Etourneau's result by giving sufficient conditions in terms of the vertex degrees for G to be dp -connected.