A 2-factor with Short Cycles Passing Through Specified Independent Vertices in Graph
โ Scribed by Jiuying Dong
- Book ID
- 106047721
- Publisher
- Springer Japan
- Year
- 2008
- Tongue
- English
- Weight
- 136 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract A weighted graph is one in which every edge __e__ is assigned a nonnegative number, called the weight of __e__. The sum of the weights of the edges incident with a vertex ฯ is called the weighted degree of ฯ . The weight of a cycle is defined as the sum of the weights of its edges. In th
## For a graph G and an integer an independent set of vertices in G}. Enomoto proved the following theorem. Let s โฅ 1 and let G be a (s + 2)-connected graph. Then G has a cycle of length โฅ min{|V (G)|, ฯ 2 (G) -s} passing through any path of length s. We generalize this result as follows. Let k โฅ
We prove the following theorem: For a connected noncomplete graph Then through each edge of G there passes a cycle of length โฅ min{|V (G)|, ฯ(G) -1}.