The base-cobase graph of the regular matroid R10 is bipartite, giving the first negative answer to the Farber-Richter-Shank Hamiltonian connectivity problem, while wheels and whirls are shown Hamiltonian connected; the separate series-parallel lattice path result relies on a false lemma.
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Hamiltonian connectivity of some base-cobase graphs
The base-cobase graph of the regular matroid R10 is bipartite, giving the first negative answer to the Farber-Richter-Shank Hamiltonian connectivity problem, while wheels and whirls are shown Hamiltonian connected; the separate series-parallel lattice path result relies on a false lemma.