Name
Abstract | ||
|---|---|---|
A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e"1,e"2,...,e"n) such that ({e"1,e"2,...,e"k},{e"k"+"1,e"k"+"2,...,e"n}) is a 3-separation for all k in {3,4,...,n-3}. In this paper, we consider the possible sequential orderings that such a matroid can have. In particular, we prove that M essentially has two fixed ends, each of which is a maximal segment, a maximal cosegment, or a maximal fan. We also identify the possible structures in M that account for different sequential orderings of E(M). These results rely on an earlier paper of the authors that describes the structure of equivalent non-sequential 3-separations in a 3-connected matroid. Those results are extended here to describe the structure of equivalent sequential 3-separations. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.ejc.2005.10.005 | Eur. J. Comb. |
Keywords | DocType | Volume |
maximal fan,maximal cosegment,3-connected matroids,equivalent non-sequential,different sequential ordering,earlier paper,equivalent sequential 3-separations,ground set e,path width,3-connected matroid,maximal segment,possible sequential ordering | Journal | 28 |
Issue | ISSN | Citations |
3 | 0195-6698 | 9 |
PageRank | References | Authors |
0.81 | 5 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rhiannon Hall | 1 | 48 | 7.55 |
| James Oxley | 2 | 194 | 24.39 |
| Charles Semple | 3 | 432 | 47.99 |