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Research Article | Open Access

The linear k-arboricity of digraphs

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 510520, 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 linear k-diforests needed to partition the arcs of D. In this paper, we study the linear k-arboricity for digraphs, and determine the linear 3-arboricity and linear 2-arboricity for symmetric complete digraphs and symmetric complete bipartite digraphs.

Keywords

linear k-arboricitydigraphssymmetric complete digraphssymmetric complete bipartite digraphs
CLC number: 05C70, 05C38

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4137-4152
DOI: 10.3934/math.2022229

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Cite this article:
Zhou X, Yang C, He W. The linear k-arboricity of digraphs. AIMS Mathematics, 2022, 7(3): 4137-4152. https://doi.org/10.3934/math.2022229

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Received: 02 July 2021
Revised: 25 November 2021
Accepted: 10 December 2021
Published: 15 March 2021
©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)