On vertex-degree restricted subgraphs in polyhedral graphs Original Research Article

First a brief survey of known facts is given. Main result of this paper: every polyhedral (i.e. 3-connected planar) graph G with minimum degree at least 4 and order at least k (k⩾4) contains a connected subgraph on k vertices having degrees (in G) at most 4k−1, the bound 4k−1 being best possible.