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On linear arboricity of 10-regular graphs. (English) Zbl 0612.05050

The linear arboricity of a graph G is the minimal number of linear forests whose union is G. Akiyama, Exoo and Harary expressed the conjecture that the linear arboricity of an r-regular graph is equal to \((r+1)/2\). The conjecture has already been proved for \(r=2,3,4,5,6\) and 8. In this paper it is verified for \(r=10\).

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C05 Trees
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References:

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