Mader proved that every 2-connected simple graph G with minimum degree d exceeding three has a cycle C, the deletion of whose edges leaves a 2-connected graph. Jackson extended this by showing that C may be chosen to avoid any nominated edge of G and to have length at least d-1. This article proves
On matroid separations of graphs
β Scribed by Klaus Truemper
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 308 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Let K be a connected and undirected graph, and M be the polygon matroid of K . Assume that, for some k 2 1, the matroid M is kseparable and k-connected according to the matroid separability and connectivity definitions of W. T. Tutte. In this paper we classify the matroid kseparations of M in terms of subgraphs of K .
π SIMILAR VOLUMES
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
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