Brylawski and Seymour independently proved that if M is a connected matroid with a connected minor N, and e ∈ E(M) − E(N), then M\e or M/e is connected having N as a minor. This paper proves an analogous but somewhat weaker result for 2-polymatroids. Specifically, if M is a connected 2-polymatroid with a proper connected minor N, then there is an element e of E(M) − E(N) such that M\e or M/e is connected having N as a minor. We also consider what can be said about the uniqueness of the way in which the elements of E(M) − E(N) can be removed so that connectedness is always maintained.
Publication Source (Journal or Book title)
Electronic Journal of Combinatorics
Gershkoff, Z., & Oxley, J. (2019). A note on the connectivity of 2-polymatroid minors. Electronic Journal of Combinatorics, 26 (4) https://doi.org/10.37236/8369