Matroid basis graph: Counting Hamiltonian cycles
arXiv:1608.02635 · doi:10.1007/s00373-019-02011-8
Abstract
We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform 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.
Reformulation of Propositions 7 and 8. Lemmas 9 and 10, and Theorem 11 are combined in the current Theorem 9