Hamilton circles in infinite planar graphs

A circle in a graph G is a homeomorphic image of the unit circle in the Freudenthal compactification of G, a topological space formed from G and the ends of G. Bruhn conjectured that every locally finite 4-connected planar graph G admits a Hamilton circle, a circle containing all points in the Freudenthal compactification of G that are vertices and ends of G. We prove this conjecture for graphs with no dividing cycles. In a plane graph, a cycle C is said to be dividing if each closed region of the plane bounded by C contains infinitely many vertices.