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Linear Arboricity and Linear k-Arboricity of Regular Graphs

✍ Scribed by Noga Alon; V. J. Teague; N. C. Wormald

Book ID
105745124
Publisher
Springer Japan
Year
2001
Tongue
English
Weight
86 KB
Volume
17
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES

The linear arboricity of some regular gr
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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

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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

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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 βˆ†. The conjecture has been proved to be true for graphs having βˆ† =

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## Abstract The linear vertex‐arboricity ρ(__G__) of a graph __G__ is defined to be the minimum number of subsets into which the vertex set of __G__ can be partitioned such that each subset induces a linear forest. In this paper, we give the sharp upper and lower bounds for the sum and product of l