Abstract
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.
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Acknowledgements
Research partially supported by CAPES (MATH-AmSud 18-MATH-01), CNPq (Proc. 308116/2016-0 and 456792/2014-7), FAPESP (Proc. 2012/24597-3, Proc. 2013/03447-6, and Proc. 2015/10323-7), PICS (Grant PICS06316), PRODEP (DSA/103.5/16/10419), and Project MaCLinC of NUMEC/USP.
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Fernandes, C.G., Hernández-Vélez, C., de Pina, J.C. et al. Counting Hamiltonian Cycles in the Matroid Basis Graph. Graphs and Combinatorics 35, 539–550 (2019). https://doi.org/10.1007/s00373-019-02011-8
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DOI: https://doi.org/10.1007/s00373-019-02011-8