Matroid basis graph: Counting Hamiltonian cycles
Combinatorics
2019-04-29 v2
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.
Cite
@article{arxiv.1608.02635,
title = {Matroid basis graph: Counting Hamiltonian cycles},
author = {Cristina G. Fernandes and César Hernández-Vélez and José C. de Pina and Jorge Luis Ramírez Alfonsín},
journal= {arXiv preprint arXiv:1608.02635},
year = {2019}
}
Comments
Reformulation of Propositions 7 and 8. Lemmas 9 and 10, and Theorem 11 are combined in the current Theorem 9