𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Uncontractable 4-connected graphs

✍ 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.

✦ Synopsis


Abstract

The only uncontractable 4‐connected graphs are C^2^~n~ for n β‰₯ 5 and the line graphs of the cubic cyclically 4‐connected graphs.


πŸ“œ SIMILAR VOLUMES


Minimally 4-edge# -connected graphs
✍ Bernard Peroche; Christine Virlouvet πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 650 KB

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

All 4-connected Line Graphs of Claw Free
✍ Matthias Kriesell πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 109 KB

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.

Minors of quasi 4-connected graphs
✍ Themistocles Politof; A. Satyanarayana πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 744 KB

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

Unavoidable parallel minors of 4-connect
✍ Carolyn Chun; Guoli Ding; Bogdan Oporowski; Dirk Vertigan πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 154 KB

## 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 4‐connected graph of sufficiently high order contains a parallel minor isomorphic to a variation of __K__~4,__k

Edge-reconstruction of 4-connected plana
✍ S. Fiorini; J. Lauri πŸ“‚ Article πŸ“… 1982 πŸ› John Wiley and Sons 🌐 English βš– 482 KB πŸ‘ 2 views

## Abstract The object of this paper is to show that 4‐connected planar graphs are uniquely determined from their collection of edge‐deleted subgraphs.

The structure of quasi 4-connected graph
✍ Themistocles Politof; A. Satyanarayana πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 646 KB

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