Constructive characterizations of 3-connected matroids of path width three

Authors:
Brian Beavers;James Oxley
Affiliations:
Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, TX, USA;Mathematics Department, Louisiana State University, Baton Rouge, LA, USA
Venue:
European Journal of Combinatorics
Year:
2008

Citing 4
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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.