Name
Abstract | ||
|---|---|---|
Tutte defined a k-separation of a matroid M to be a partition (A, B) of the ground set of M such that |A|, |B| ≥ k and r(A) + r(B) - r(M) k. If, for all m n, the matroid M has no m- separations, then M is n-connected. Earlier, Whitney showed that (A, B) is a 1-separation of M if and only if A is a union of 2-connected components of M. When M is 2-connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2- separations. When M is 3-connected, this paper describes a tree decomposition of M that displays, up to a certain natural equivalence, all non-trivial 3-separations of M. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1016/j.jctb.2004.03.006 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
3-connected matroid,3-connected matroids,3-separation,certain natural equivalence,tree decomposition,matroid m,tutte connectivity,2-connected component,m n,05b35,connected component | Matroid,Discrete mathematics,Combinatorics,Tree decomposition,Equivalence (measure theory),Partition (number theory),Mathematics | Journal |
Volume | Issue | ISSN |
92 | 2 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
27 | 2.48 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James Oxley | 1 | 194 | 24.39 |
| Charles Semple | 2 | 432 | 47.99 |
| Geoff Whittle | 3 | 471 | 57.57 |