Name
Abstract | ||
|---|---|---|
Seymour's decomposition theorem [J. Combin. Theory Ser. B, 28 (1980), pp. 305-359] for regular matroids states that any matroid representable over both $\mathrm{GF}(2)$ and $\mathrm{GF}(3)$ can be obtained from matroids that are graphic, cographic, or isomorphic to $R_{10}$ by 1-, 2-, and 3-sums. It is hoped that similar characterizations hold for other classes of matroids, notably for the class of near-regular matroids. Suppose that all near-regular matroids can be obtained from matroids that belong to a few basic classes through $k$-sums. Also suppose that these basic classes are such that, whenever a class contains all graphic matroids, it does not contain all cographic matroids. We show that, in that case, 3-sums will not suffice. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/090759616 | SIAM Journal on Discrete Mathematics |
Keywords | Field | DocType |
theory ser,graphic matroids,cographic matroids,basic class,near-regular matroids,regular matroids state,j. combin,similar characterization,decomposition theorem,matroid representable | Matroid,Graphics,Discrete mathematics,Obstacle,Combinatorics,Decomposition method (constraint satisfaction),Isomorphism,Decomposition theorem,Graphic matroid,Mathematics | Journal |
Volume | Issue | ISSN |
25 | 1 | 0895-4801 |
Citations | PageRank | References |
2 | 0.65 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dillon Mayhew | 1 | 102 | 18.63 |
| Geoff Whittle | 2 | 471 | 57.57 |
| Stefan H. M. van Zwam | 3 | 60 | 8.60 |