Name
Abstract | ||
|---|---|---|
In an earlier paper, we proved that an internally 4-connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. We refine this result, by giving detailed descriptions of the operations required to produce the internally 4-connected minor. Each of these operations is top-down, in that it produces a smaller minor from the original. We also describe each as a bottom-up operation, constructing a larger matroid from the original, and we give necessary and sufficient conditions for each of these bottom-up moves to produce an internally 4-connected binary matroid. From this, we derive a constructive method for generating all internally 4-connected binary matroids. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.aam.2012.03.005 | Advances in Applied Mathematics |
Keywords | Field | DocType |
sufficient condition,constructive method,earlier paper,bottom-up move,4-connected binary matroid,bottom-up operation,4-connected binary matroids,detailed description,4-connected proper minor,larger matroid | Matroid,Discrete mathematics,Combinatorics,Constructive,Matroid partitioning,Graphic matroid,Binary matroid,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
50 | 1 | 0196-8858 |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carolyn Chun | 1 | 25 | 8.25 |
| Dillon Mayhew | 2 | 102 | 18.63 |
| James Oxley | 3 | 194 | 24.39 |