The radius of -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 ) ≤ p 6 + 5 l 6 + 2 3 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.