Name
Abstract | ||
|---|---|---|
An essential element of a 3-connected matroid M is one for which neither the deletion nor the contraction is 3-connected. Tutte's Wheels and Whirls Theorem proves that the only 3-connected matroids in which every element is essential are the wheels and whirls. In an earlier paper, the authors showed that a 3-connected matroid with at least one non-essential element has at least two such elements. This paper completely determines all 3-connected matroids with exactly two non-essential elements. Furthermore, it is proved that every 3-connected matroid M for which no single-element contraction is 3-connected can be constructed from a similar such matroid whose rank equals the rank in M of the set of elements e for which the deletion M\e is 3-connected. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1007/s003730050016 | Graphs and Combinatorics |
Keywords | Field | DocType |
essential element,fan. 1,. matroid,3-connected,theorem proving | Matroid,Graph,Discrete mathematics,Combinatorics,Oriented matroid,Matroid partitioning,Graphic matroid,Weighted matroid,Mathematics | Journal |
Volume | Issue | ISSN |
16 | 2 | 0911-0119 |
Citations | PageRank | References |
7 | 0.88 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James Oxley | 1 | 397 | 57.57 |
| Haidong Wu | 2 | 7 | 0.88 |
| HD Wu | 3 | 7 | 0.88 |