Title

A note on the connectivity of 2-polymatroid minors

Document Type

Article

Publication Date

1-1-2019

Abstract

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

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