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Unavoidable Minors of Large 3-Connected Matroids

✍ Scribed by Guoli Ding; Bogdan Oporowski; James Oxley; Dirk Vertigan

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
704 KB
Volume
71
Category
Article
ISSN
0095-8956

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✦ Synopsis

This paper proves that, for every integer n exceeding two, there is a number N(n) such that every 3-connected matroid with at least N(n) elements has a minor that is isomorphic to one of the following matroids: an (n+2)-point line or its dual, the cycle or cocycle matroid of K 3, n , the cycle matroid of a wheel with n spokes, a whirl of rank n, or an n-spike. A matroid is of the last type if it has rank n and consists of n three-point lines through a common point such that, for all k in [1, 2, ..., n&1], the union of every set of k of these lines has rank k+1.

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