The linear k-arboricity of symmetric directed trees

The linear k-arboricity of symmetric directed trees

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A linear k-diforest is a directed forest in which every connected component is a directed path of length at most k.The linear k-arboricity of Sous Vide a digraph D is the minimum number of arc-disjoint Kaleidoscopes linear k-diforests whose union covers all the arcs of D.In this paper, we study the linear k-arboricity for symmetric directed trees and fully determine the linear 2-arboricity for all symmetric directed trees.