Covering and packing in graphs. III: Cyclic and acyclic invariants

A Jin，G Exoo，F Harary - 《Mathematica Slovaca》

The linear arboricity of some regular graphs

We 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. We also determine the linear arboricity of 6-regular graphs and 8-regular graphs. These res...

H Enomoto，B Péroche - 《Journal of Graph Theory》

Linear 3-arboricity of the Balanced Complete Multipartite Graph

A linear k-forest is a graph whose components are paths with lengths at most k. The minimum number of linear k-forests needed to decompose a graph G is the...

Chih-Hung，Yen，Hung-Lin，... - 《Journal of Combinatorial Mathematics & Combinatorial Computing》

A status on the linear arboricity

In a inear forest, each component is a path. The linear arboricity ≡(G) of a graph G is defined in Harary [8] as the minimum number of linear forests whose union is G. This invariant first arose in a

A Jin - Springer-Verlag

On the linear k-arboricity of cubic graphs

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 connecte...

JNC Wormald - 《Discrete Mathematics》

Linear Arboricity and Linear k-Arboricity of Regular Graphs

We find upper bounds on the linear k-arboricity of d-regular graphs using a probabilistic argument. For small k these bounds are new. For large k they blen...

N Alon，VJ Teague，NC Wormald - 《Graphs & Combinatorics》

On the linear arboricity of planar graphs

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 t...

J Wu - 《Journal of Graph Theory》

On the linear k -arboricity of K n and K n , n

A linear k-forest of a undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity of G, denoted by la...

BL Chen，KC Huang - 《Discrete Mathematics》

On the linear (n-1)-arboricity of Kn(m)

A linear k-forest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity of G, denoted by l...

X Bing，L Zuo - Elsevier Science Publishers B. V.

The linear 3-arboricity of K n , n and K n

A linear k -forest is a forest whose components are paths of length at most k . The linear k -arboricity of a graph G   , denoted by la k (G) la k ( G ) mathContainer Loading Mathjax , is the least number of linear k -forests needed t...

Hung-Lin Fu a，Kuo-Ching Huang b，Chih-Hung Yen c - 《Discrete Mathematics》