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 matro
On 3-connected minors of 3-connected matroids and graphs
✍ Scribed by João Paulo Costalonga
- Book ID
- 113582384
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 265 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0195-6698
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📜 SIMILAR VOLUMES
We show that, for every integer n greater than two, there is a number N such that every 3-connected binary matroid with at least N elements has a minor that is isomorphic to the cycle matroid of K 3, n , its dual, the cycle matroid of the wheel with n spokes, or the vector matroid of the binary matr
An element e of a 3-connected matroid M is essential if neither the deletion M\e nor the contraction M/e is 3-connected. Tutte's Wheels and Whirls Theorem proves that the only 3-connected matroids in which every element is essential are the wheels and whirls. In this paper, we consider those 3-conne