The linear arboricity of graphs
β Scribed by N. Alon
- Book ID
- 112891802
- Publisher
- The Hebrew University Magnes Press
- Year
- 1988
- Tongue
- English
- Weight
- 636 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
W e prove that the linear arboricity of every 5-regular graph is 3. That is, the edges of any 5-regular graph are covered by three linear forests. W e also determine the linear arboricity of 6-regular graphs and 8-regular graphs. These results improve the known upper bounds for the linear arboricity
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree β. The conjecture has been proved to be true for graphs having β =
Bermond et al. [2] conjectured that the edge set of a cubic graph G can be partitioned into two k-linear forests, that is to say two forests whose connected components are paths of length at most k, for all k >/5. We shall prove a weaker result that the statement is valid for all k/> 18. All graphs