This paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U 2, 6 -, U 4, 6 -, P 6 -, F & 7 -, or (F & 7 )\*-minors. Explicitly, these
The Excluded Minors for GF(4)-Representable Matroids
β Scribed by J.F. Geelen; A.M.H. Gerards; A. Kapoor
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 547 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
There are exactly seven excluded minors for the class of GF(4)-representable matroids.
π SIMILAR VOLUMES
In this article it is shown that every 4-connected graph that does not contain a minor isomorphic to the octahedron is isomorphic to the square of an odd cycle.
## Abstract Let __G__ be the unique 4βconnected simple graph obtained by adding an edge to the Octahedron. Every 4βconnected graph that does not contain a minor isomorphic to __G__ is either planar or the square of an odd cycle. Β© 2007 Wiley Periodicals, Inc. J Graph Theory 57: 124β130, 2008
We give a simple proof of the fact (which follows from the Robertson Seymour theory) that a graph which is minimal of genus g cannot contain a subdivision of a large grid. Combining this with the tree-width theorem and the quasi-wellordering of graphs of bounded tree-width in the Robertson Seymour t
We present a new direct proof of the Folkman-Lawrence topological representation theorem for oriented matroids of rank 3.