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arXiv · 1608.02635

Matroid basis graph: Counting Hamiltonian cycles

Cristina G. Fernandes·César Hernández-Vélez·José C. de Pina·Jorge Luis Ramírez Alfonsín
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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.

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Cristina G. Fernandes, César Hernández-Vélez, José C. de Pina, Jorge Luis Ramírez Alfonsín. 2017-01-18. Matroid basis graph: Counting Hamiltonian cycles. https://doi.org/10.1007/s00373-019-02011-8

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