𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Contractible Edges in a 4-Connected Graph with Vertices of Degree Greater Than Four

✍ Scribed by Kiyoshi Ando; Yoshimi Egawa

Publisher
Springer Japan
Year
2007
Tongue
English
Weight
191 KB
Volume
23
Category
Article
ISSN
0911-0119

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Vertices of degree 6 in a contraction cr
Vertices of degree 6 in a contraction critically 6-connected graph
✍ Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 378 KB

An edge of a 6-connected graph is said to be 6-contractible if the contraction of the edge results in a 6-connected graph. A contraction critically 6-connected graph is a 6-connected graph with no 6-contractible edge. We prove that each contraction critically 6-connected graph G has at least 1 7 |V

A Degree Sum Condition for the Existence
A Degree Sum Condition for the Existence of a Contractible Edge in a ΞΊ-Connected Graph
✍ Matthias Kriesell πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 184 KB

It is known that a noncomplete }-connected graph of minimum degree of at least w 5} 4 x contains a }-contractible edge, i.e., an edge whose contraction yields again a }-connected graph. Here we prove the stronger statement that a noncomplete }-connected graph for which the sum of the degrees of any