Contractible edges in a k-connected graph (K1 + P4)-free graph
β Scribed by Kiyoshi Ando
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 215 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1571-0653
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π SIMILAR VOLUMES
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
## Abstract For a graph __G__ we define a graph __T__(__G__) whose vertices are the triangles in __G__ and two vertices of __T__(__G__) are adjacent if their corresponding triangles in __G__ share an edge. Kawarabayashi showed that if __G__ is a __k__βconnected graph and __T__(__G__) contains no ed