2019/08/27 by Gershkoff, Zachary, Oxley, James
#05B35 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1908.09971
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 \backslash 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 \backslash 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.