## Abstract An edge of a 3βconnected graph is said to be __contractible__ if its contraction results in a 3βconnected graph. In this paper, a covering of contractible edges is studied. We give an alternative proof to the result of Ota and Saito (__Scientia__ (A) 2 (1988) 101β105) that the set of co
Contractible edges in 3-connected graphs
β Scribed by Kiyoshi Ando; Hikoe Enomoto; Akira Saito
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 371 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract It is shown that if __G__ is a 3βconnected graph with |__V(G)__| β₯ 10, then, with the exception of one infinite class based on __K__~3,__p__~, it takes at least four vertices to cover the set of contractible edges of __G__. Β© 1993 John Wiley & Sons, Inc.
We present a reduction theorem for the class of all finite 3-connected graphs which does not make use of the traditional contraction of certain connected subgraphs. ## 1998 Academic Press Contractible edges play an important role in the theory of 3-connected graphs. Besides the famous wheel theore
We show that if G is a 3-connected graph of order at least seven, then every longest path between distinct vertices in G contains at least two contractible edges. An immediate corollary is that longest cycles in such graphs contain at least three contractible edges. We consider only finite undirect
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