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Article Dans Une Revue Graphs and Combinatorics Année : 2019

Counting Hamiltonian Cycles in the Matroid Basis Graph

Résumé

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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Dates et versions

hal-02070575 , version 1 (18-03-2019)

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Cristina G. Fernandes, César Hernández-Vélez, José C de Pina, Jorge Luis Ramírez Alfonsín. Counting Hamiltonian Cycles in the Matroid Basis Graph. Graphs and Combinatorics, 2019, 35 (2), pp.539-550. ⟨10.1007/s00373-019-02011-8⟩. ⟨hal-02070575⟩
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