On the hamiltonicity of a planar graph and its vertex‐deleted subgraphs

Tutte proved that every planar 4‐connected graph is hamiltonian. Thomassen showed that the same conclusion holds for the superclass of planar graphs with minimum degree at least 4 in which all vertex‐deleted subgraphs are hamiltonian. We here prove that if in a planar n $n$‐vertex graph with minimum degree at least 4 at least n−5 $n-5$ vertex‐deleted subgraphs are hamiltonian, then the graph contains two hamiltonian cycles, but that for every c