Cycles in 3-Connected Cubic Planar Graphs

Let G be a 3-connected cubic planar graph and let A be a subset of the vertices of G. In order to find the largest set A through which there exists a cycle, it is currently necessary to determine those graphs G for which there exists a cycle through A avoiding a given edge e of G. We consider the cases [A] ≤ 12. As a consequence we show that any 17 vertices lie on a cycle in a 3-connected cubic planar graph, while any 20 vertices lie on a cycle in such graphs if the result is true for the cyclically 4-edge-connected ones.