Hamiltonicity of planar graphs with a forbidden minor
Mark N. Ellingham, Emily A. Marshall, Kenta Ozeki, Shoichi Tsuchiya · Journal of Graph Theory · 2018
Abstract Tutte showed that ‐connected planar graphs are Hamiltonian, but it is well known that ‐connected planar graphs need not be Hamiltonian. We show that ‐minor‐free ‐connected planar graphs are Hamiltonian. This does not extend to ‐minor‐free ‐connected graphs in general, as shown by the Petersen graph, and does not extend to ‐minor‐free ‐connected planar graphs, as we show by an infinite family of examples.