## Abstract A graph __G__ = (__V__, __E__) is called weakly four‐connected if __G__ is 4‐edge‐connected and __G__ − __x__ is 2‐edge‐connected for all __x__ ∈ __V__. We give sufficient conditions for the existence of ‘splittable’ vertices of degree four in weakly four‐connected graphs. By using thes
A recursive characterization of the 4-connected graphs
✍ Scribed by Nicola Martinov
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 244 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
We present a complete description of the set of 4-connected contraction-critical graphs.
📜 SIMILAR VOLUMES
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
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
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.
## Abstract A graph __G__ is critically 2‐connected if __G__ is 2‐connected but, for any point __p__ of __G, G — p__ is not 2‐connected. Critically 2‐connected graphs on __n__ points that have the maximum number of lines are characterized and shown to be unique for __n__ ⩾ 3, __n__ ≠ 11.