强边连通有向图的正生成集的刻画

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-05-19 DOI:10.1016/j.dam.2025.05.025

Denis Cornaz, Sébastien Kerleau, Clément W. Royer

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引用次数: 0

摘要

正生成集（pss）是通过非负线性组合张成给定线性空间的向量族。尽管某些类别的pss被很好地理解，但pss的完整特征仍然难以捉摸。在本文中，我们探讨了正生成集与强边连通有向图之间的关系，因为前者可以看作是后者的推广。我们利用这种联系来定义一个受有向图理论的耳分解启发的正生成集的分解结构。

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A characterization of positive spanning sets with ties to strongly edge-connected digraphs

Positive spanning sets (PSSs) are families of vectors that span a given linear space through non-negative linear combinations. Despite certain classes of PSSs being well understood, a complete characterization of PSSs remains elusive. In this paper, we explore a relatively understudied relationship between positive spanning sets and strongly edge-connected digraphs, in that the former can be viewed as a generalization of the latter. We leverage this connection to define a decomposition structure for positive spanning sets inspired by the ear decomposition from digraph theory.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.