Name
Abstract | ||
|---|---|---|
Let M be a 3-connected matroid, and let N be a 3-connected minor of M. A pair {x1,x2}⊆E(M) is N-detachable if one of the matroids M/x1/x2 or M\x1\x2 is both 3-connected and has an N-minor. This is the second in a series of three papers where we describe the structures that arise when it is not possible to find an N-detachable pair in M. In the first paper in the series, we showed that, under mild assumptions, either M has an N-detachable pair, M has one of three particular 3-separators that can appear in a matroid with no N-detachable pairs, or there is a 3-separating set X with certain strong structural properties. In this paper, we analyse matroids with such a structured set X, and prove that they have either an N-detachable pair, or one of five particular 3-separators that can appear in a matroid with no N-detachable pairs. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.jctb.2020.07.008 | Journal of Combinatorial Theory, Series B |
Keywords | DocType | Volume |
3-connected,Splitter theorem,Matroid structure | Journal | 149 |
ISSN | Citations | PageRank |
0095-8956 | 1 | 0.40 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nick Brettell | 1 | 1 | 0.73 |
| Geoff Whittle | 2 | 471 | 57.57 |
| Alan Williams | 3 | 1 | 1.07 |