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Linear arboricity and linear $$k$$-arboricity of regular graphs. (English) Zbl 0982.05079
The linear arboricity $$\text{la}(G)$$ (respectively, $$k$$-linear arboricity $$\text{la}_k(G)$$), of a graph $$G$$ is the minimum number of forests, each of whose components is a path (respectively, each of whose components is a path of length at most $$k$$) required to partition $$E(G)$$; $$\text{la}_k(d)$$ is defined to be $$\max_{G \text{ is }d}-regular$$

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C35 Extremal problems in graph theory 05C38 Paths and cycles 05C05 Trees
##### Keywords:
linear arboricity
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