It is proved that if G is a k-connected graph which does not contain K - 4 , then G has an edge e or a triangle T such that the graph obtained from G by connecting e or by contracting T is still k-connected. By using this theorem, we prove some theorems which are generalizations of earlier work. In
Contractible edges in minimally k-connected graphs
β Scribed by Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 420 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
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## Abstract For an integer __l__β>β1, the __l__βedgeβconnectivity of a connected graph with at least __l__ vertices is the smallest number of edges whose removal results in a graph with __l__ components. A connected graph __G__ is (__k__, __l__)βedgeβconnected if the __l__βedgeβconnectivity of __G_