Nested matroids were introduced by Crapo in 1965 and have appeared frequently in the literature since then. A flat of a matroid M is Hamiltonian if it has a spanning circuit. A matroid M is nested if and only if its Hamiltonian flats form a chain under inclusion; M is laminar if and only if, for every 1-element independent set X, the Hamiltonian flats of M containing X form a chain under inclusion. We generalize these notions to define the classes of k-closure-laminar and k-laminar matroids. This paper focuses on structural properties of these classes noting that, while the second class is always minor-closed, the first is if and only if k≤3. The main results are excluded-minor characterizations of the classes of 2-laminar and 2-closure-laminar matroids.
Publication Source (Journal or Book title)
European Journal of Combinatorics
Fife, T., & Oxley, J. (2019). Generalized laminar matroids. European Journal of Combinatorics, 79, 111-122. https://doi.org/10.1016/j.ejc.2018.12.005