Name
Abstract | ||
|---|---|---|
We consider various applications of our characterization of the internally
4-connected binary matroids with no M(K3,3)-minor. In particular, we
characterize the internally 4-connected members of those classes of binary
matroids produced by excluding any collection of cycle and bond matroids of
K3,3 and K5, as long as that collection contains either M(K3,3) or M*(K3,3). We
also present polynomial-time algorithms for deciding membership of these
classes, where the input consists of a matrix with entries from GF(2). In
addition we characterize the maximum-sized simple binary matroids with no
M(K3,3)-minor, for any particular rank, and we show that a binary matroid with
no M(K3,3)-minor has a critical exponent over GF(2) of at most four. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.jctb.2017.03.005 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
critical exponent | Matroid,Graph,Discrete mathematics,Combinatorics,Dual polyhedron,Graphic matroid,Binary matroid,Critical exponent,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
125 | C | 0095-8956 |
Citations | PageRank | References |
0 | 0.34 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dillon Mayhew | 1 | 102 | 18.63 |
| Gordon Royle | 2 | 39 | 5.05 |
| Geoff Whittle | 3 | 471 | 57.57 |