The r-depth of a matroid

Abstract

We introduce the concept of depth and r-depth of a matroid M, proving that the sequence of the r-depths is the conjugate partition of the rank partition of M. The notion of quasitransversal is defined and its properties stated. We also present connections between the concept of r-depth, the quasi-transversals of M and the circuits of the kth power of M.

DOI: 10.1016/0012-365X(93)E0209-M

Cite this paper

@article{Silva1995TheRO, title={The r-depth of a matroid}, author={J. A. Dias da Silva and Am{\'e}lia Fonseca}, journal={Discrete Mathematics}, year={1995}, volume={141}, pages={85-93} }