On packing minors into connected matroids
Let N be a matroid with k connected components and M be a minor-minimal connected matroid having N as a minor. This note proves that |E(M) - E(N)| is at most 2k - 2 unless N or its dual is free, in which case |E(M) - E(N)| ≤k - 1. Examples are given to show that these bounds are best possible for all choices for N. A consequence of the main result is that a minimally connected matroid of rank r and maximum circuit size c has at most 2r - c + 2 elements. This bound sharpens a result of Murty. © 1998 Elsevier Science B.V. All rights reserved.
Publication Source (Journal or Book title)
Lemos, M., & Oxley, J. (1998). On packing minors into connected matroids. Discrete Mathematics, 189 (1-3), 283-289. https://doi.org/10.1016/S0012-365X(98)00055-7