Graphs and Combinatorics

, Volume 35, Issue 2, pp 539–550 | Cite as

Counting Hamiltonian Cycles in the Matroid Basis Graph

  • Cristina G. Fernandes
  • César Hernández-VélezEmail author
  • José C. de Pina
  • Jorge Luis Ramírez Alfonsín
Original Paper


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.


Matroid basis graph Generalized Catalan matroid Hamiltonian cycle 

Mathematics Subject Classification

05B35 05C38 05C45 



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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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Facultad de CienciasUniversidad Autónoma de San Luis PotosíSan Luis PotosiMéxico
  3. 3.IMAG, Univ. Montpellier, CNRSMontpellierFrance

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