Name
Abstract | ||
|---|---|---|
A matroid M is sequential or has path width 3 if M is 3-connected and its ground set has a sequential ordering, that is, an ordering (e"1,e"2,...,e"n) such that ({e"1,e"2,...,e"k},{e"k"+"1,e"k"+"2,...,e"n}) is a 3-separation for all k in {3,4,...,n-3}. This paper proves that every sequential matroid is easily constructible from a uniform matroid of rank or corank two by a sequence of moves each of which consists of a slight modification of segment-cosegment or cosegment-segment exchange. It is also proved that if N is an n-element sequential matroid, then N is representable over all fields with at least n-1 elements; and there is an attractive family of self-dual sequential 3-connected matroids such that N is a minor of some member of this family. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.ejc.2007.10.004 | Eur. J. Comb. |
Keywords | Field | DocType |
n-element sequential matroid,attractive family,cosegment-segment exchange,3-connected matroids,sequential matroid,self-dual sequential,matroid m,constructive characterization,path width,uniform matroid,ground set,n-1 element,gain control,tree decomposition | Matroid,Discrete mathematics,Combinatorics,Constructive,Matroid partitioning,Graphic matroid,Uniform matroid,Mathematics | Journal |
Volume | Issue | ISSN |
29 | 7 | 0195-6698 |
Citations | PageRank | References |
3 | 0.54 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Brian Beavers | 1 | 4 | 0.97 |
| James Oxley | 2 | 20 | 4.05 |