Name
Abstract | ||
|---|---|---|
Adding elements to matroids can be fraught with difficulty. In the Vamos matroid V-8, there are four pairs X-1, X-2, X-3, and X-4 that partition E(V-8) such that (X-1 boolean OR X-2, X-3 boolean OR X-4) is a 3-separation while exactly three of the local connectivities Pi (X-1, X-3), Pi (X-1, X-4), (X-2, X-3), and Pi (X-2, X-4) are one, with the fourth being zero. As is well known, there is no extension of V-8 by a nonloop element p such that X-j boolean OR(p) is a circuit for all j. This paper proves that a matroid can be extended by a fixed element in the guts of a 3-separation provided no Vamos-like structure is present. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/18M1187155 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | Field | DocType |
matroid extension,Vamos matroid | Matroid,Discrete mathematics,Combinatorics,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 1 | 0895-4801 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James Oxley | 1 | 397 | 57.57 |