The radius of k-connected planar graphs with bounded faces

We prove that if G is a 3-connected plane graph of order p, maximum face length l and radius rad(G), then the bound rad(G)≤p6+5l6+23 holds. For constant l, our bound is shown to be asymptotically sharp and improves on a bound by Harant (1990) [6]. Furthermore we extend these results to 4- and 5-connected planar graphs.