An edge e in a 3-connected graph G is contractible if the contraction G/e is still 3-connected. The problem of bounding the number of contractible edges in a 3-connected graph has been studied by numerous authors. In this paper, the corresponding problem for matroids is considered and new graph res
On elements in small cocircuits in minimally k-connected graphs and matroids
โ Scribed by Talmage James Reid; Haidong Wu
- Book ID
- 108315673
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 107 KB
- Volume
- 243
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In [15] , Thomassen proved that any triangle-free k-connected graph has a contractible edge. Starting with this result, there are several results concerning the existence of contractible elements in k-connected graphs which do not contain specified subgraphs. These results extend
Let G be a minimally k-edge-connected simple graph and u\*(G) be the number of vertices of degree k in G. proved that (i) uk(G) 2 l(jGl -1)/(2k + l)] + k + 1 for even k, and (ii) uI(G) 2 [lGl/(k + l)] + k for odd k 35 and u,(G) 2 lZlGl/(k + l)] + k -2 for odd k 27, where ICI denotes the number of v