Counting Hamiltonian Cycles in the Matroid Basis Graph

We present superfactorial and exponential lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graph of generalized Catalan, uniform, and graphic matroids. All lower bounds were obtained by a common general strategy based on counting appropriated cycles of length four in the corresponding matroid basis graph. © 2019, Springer Japan KK, part of Springer Nature.

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