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Research Article | Open Access

The linear k-arboricity of symmetric directed trees

Xiaoling Zhou1, Chao Yang2, Weihua He1( )
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China
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Abstract

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 a digraph D is the minimum number of arc-disjoint 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.

Keywords

linear k-arboricitydigraphsdirected treessymmetric directed treeslinear arboricity
CLC number: 05C70, 05C38

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 1603-1614
DOI: 10.3934/math.2022093

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Cite this article:
Zhou X, Yang C, He W. The linear k-arboricity of symmetric directed trees. AIMS Mathematics, 2022, 7(2): 1603-1614. https://doi.org/10.3934/math.2022093

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Received: 29 May 2021
Accepted: 26 October 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)