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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
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