Name
Abstract | ||
|---|---|---|
A sufficiently large connected matroid M contains a big circuit or a big cocircuit. Wu showed that we can ensure that M has a big circuit or a big cocircuit containing any chosen element of M. In this paper, we prove that, for a fixed connected matroid N, if M is a sufficiently large connected matroid having N as a minor, then, up to duality, either M has a big connected minor in which N is a spanning restriction and the deletion of E(N) is a large connected uniform matroid, or M has, as a minor, the 2-sum of a big circuit and a connected single-element extension or coextension of N. In addition, we find a set of unavoidable minors for the class of graphs that have a cycle and a bond with a big intersection. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/14096089X | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | Field | DocType |
unavoidable minor,connected matroid | Matroid,Graph,Discrete mathematics,Combinatorics,Matroid partitioning,Duality (optimization),Graphic matroid,Uniform matroid,Mathematics | Journal |
Volume | Issue | ISSN |
30 | 3 | 0895-4801 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carolyn Chun | 1 | 25 | 8.25 |
| Guoli Ding | 2 | 444 | 51.58 |
| Dillon Mayhew | 3 | 102 | 18.63 |
| James Oxley | 4 | 397 | 57.57 |