Reachability in graphs having linear 2-arboricity two is NL-hard

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2025-10-10 DOI:10.1016/j.ipl.2025.106611

Ronak Bhadra, Raghunath Tewari

引用次数: 0

Abstract

A linear k-diforest is a directed forest consisting of directed paths of length at most k. Linear k-arboricity of a directed graph is defined as the minimum number of linear k-diforests needed to partition the edges of the graph. We show that the problem of deciding reachability in directed graphs having linear 2-arboricity two is

NL

-hard and the same is also true for directed graphs having linear 1-arboricity three. Our proof also implies that deciding reachability in such graphs remains hard even when a decomposition into two linear 2-diforests or three linear 1-diforests is provided. We further extend our results for a more restricted notion of linear arboricity, called geometric linear arboricity.

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具有线性2-任意2的图中的可达性是NL-hard

线性k-diforest是由长度最多为k的有向路径组成的有向森林。有向图的线性k-树性定义为划分图边所需的最小线性k-diforest数。我们证明了判定具有线性2-任意性2的有向图的可达性问题是NL-hard的，对于具有线性1-任意性3的有向图也是如此。我们的证明还表明，即使提供了分解为两个线性2-双森林或三个线性1-双森林的图，也很难确定图中的可达性。我们进一步推广了线性树性的一个更严格的概念，称为几何线性树性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.