In this article, we deal with a connectivity problem stated by Maurer and Slater to characterize minimally k-edge'-connected graphs. This problem has been solved for k = 1,2 and 3, and we recall herein the results obtained. Then we give some partial results concerning the case k =4: representation o
Uncontractable 4-connected graphs
β Scribed by Nicola Martinov
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 98 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
The only uncontractable 4βconnected graphs are C^2^~n~ for n β₯ 5 and the line graphs of the cubic cyclically 4βconnected graphs.
π SIMILAR VOLUMES
Thomassen conjectured that every 4-connected line graph is hamiltonian. Here we shall see that 4-connected line graphs of claw free graphs are hamiltonian connected.
A minimal point disconnecting set S of a graph G is a nontrivial m-separator, where m=IS), if the connected components of G-S can be partitioned into two sets each of which has at least two points. A 3-connected graph is quasi 4-connected if it has no nontrivial S-separators. Let G be a quasi 4-conn
## Abstract A __parallel minor__ is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer __k__, every internally 4βconnected graph of sufficiently high order contains a parallel minor isomorphic to a variation of __K__~4,__k
## Abstract The object of this paper is to show that 4βconnected planar graphs are uniquely determined from their collection of edgeβdeleted subgraphs.
A minimal point disconnecting set S of a graph G is a nontrivial m-separator, where m = IS I, if the connected components of G -S can be partitioned into two subgraphs each of which has at least two points. A 3-connected graph is quasi 4-connected if it has no nontrivial 3separators. This paper prov