## Abstract An edge of a 5βconnected graph is said to be contractible if the contraction of the edge results in a 5βconnected graph. Let __x__ be a vertex of a 5βconnected graph. We prove that if there are no contractible edges whose distance from __x__ is two or less, then either there are two tri
On Local Structure of 9- and 10-Connected Graphs
β Scribed by S. A. Obraztsova
- Book ID
- 113072929
- Publisher
- Springer US
- Year
- 2012
- Tongue
- English
- Weight
- 466 KB
- Volume
- 184
- Category
- Article
- ISSN
- 1573-8795
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π SIMILAR VOLUMES
The local connectivity ΞΊ(u, v) of two vertices u and v in a graph G is the maximum number of internally disjoint u-v paths in G, and the connectivity of G is defined as } for all pairs u and v of vertices in G. Let Ξ΄(G) be the minimum degree of G. We call a graph G maximally connected when ΞΊ(G) = Ξ΄
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