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Similar to graphs, a Matroid $M$ is said to be Hamiltonian if there is a base $B$ of $M$ and $e \in M-B$ such that $B + e$ is a cycle of $M$. Is there any literature on this?

EDIT: Actually my interest is in finding literature on matroids with the following property:

Both $M$ and $M^*$ are Hamiltonian and they share a Hamiltonian cycle i.e. there is $C$ which is a Hamiltonian cycle of both $M$ and $M^*$

Are there any characterization of such matroids?

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  • $\begingroup$ Did you try scholar.google.com/… ? It seems to answer your question "yes": there is literature (about 8 papers) on this. Or did you have a more specific question that these papers don't answer? $\endgroup$
    – David Eppstein
    Commented Nov 23, 2013 at 5:57
  • $\begingroup$ Actually, I would like to find out if there is a characterization of Matroids $M$ with a set $C$ Hamiltonian circuit simultaneously in $M$ and $M^*$. Maybe I should make my question more specific. $\endgroup$
    – hbm
    Commented Nov 23, 2013 at 17:29

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