On 3-connected matroids
β Scribed by Manoel Lemos
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 997 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
If M is a loopless matroid in which MIX and MI Y are connected and X c~ Y is non-empty, then one easily shows that MI(X u Y) is connected. Likewise, it is straightforward to show that if G and H are n-connected graphs having at least n common vertices, then G u H is nconnected. The purpose of this n
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
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
## Abstract A wellβknown result of Tutte states that a 3βconnected graph __G__ is planar if and only if every edge of __G__ is contained in exactly two induced nonβseparating circuits. Bixby and Cunningham generalized Tutte's result to binary matroids. We generalize both of these results and give n