Name
Abstract | ||
|---|---|---|
A result of Ding, Oporowski, Oxley, and Vertigan reveals that a large 3-connected matroid M has unavoidable structure. For every n2, there is an integer f(n) so that if |E(M)|f(n), then M has a minor isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K"3","n, or U"2","n or U"n"-"2","n. In this paper, we build on this result to determine what can be said about a large structure using a specified element e of M. In particular, we prove that, for every integer n exceeding two, there is an integer g(n) so that if |E(M)|g(n), then e is an element of a minor of M isomorphic to the rank-n wheel or whirl, a rank-n spike, the cycle or bond matroid of K"1","1","1","n, a specific single-element extension of M(K"3","n) or the dual of this extension, or U"2","n or U"n"-"2","n. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.ejc.2012.01.012 | Eur. J. Comb. |
Keywords | Field | DocType |
matroid element,m isomorphic,integer g,bond matroid,3-connected minor,specific single-element extension,minor isomorphic,integer n,rank-n wheel,large structure,3-connected matroid,rank-n spike | Integer,Matroid,Discrete mathematics,Combinatorics,Isomorphism,Function composition,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 6 | 0195-6698 |
Citations | PageRank | References |
2 | 0.41 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Deborah Chun | 1 | 4 | 3.52 |
| James Oxley | 2 | 20 | 4.05 |
| Geoff Whittle | 3 | 471 | 57.57 |