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.
Graph Curve Matroids
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abstract
We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove that these matroids provide a combinatorial description of hyperplane sections of degenerate canonical curves in algebraic geometry. Our focus lies on graphs that are 2-connected and trivalent, which define identically self-dual graph curve matroids, but we also develop generalizations. Finally, we provide an algorithm to compute the graph curve matroid associated to a given graph, as well as an implementation and data of examples that can be used in Macaulay2.
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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.