The complexity of 2-vertex-connected orientation in mixed graphs

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2023-05-01 DOI:10.1016/j.disopt.2023.100774

Florian Hörsch , Zoltán Szigeti

引用次数: 0

Abstract

We consider two possible extensions of a theorem of Thomassen characterizing the graphs admitting a 2-vertex-connected orientation. First, we show that the problem of deciding whether a mixed graph has a 2-vertex-connected orientation is NP-hard. This answers a question of Bang-Jensen, Huang and Zhu. For the second part, we call a directed graph $D = (V, A)$ $2 T$ -connected for some $T \subseteq V$ if $D$ is 2-arc-connected and $D - v$ is strongly connected for all $v \in T$ . We deduce a characterization of the graphs admitting a $2 T$ -connected orientation from the theorem of Thomassen.

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混合图中2-顶点连通方向的复杂性

我们考虑托马森定理的两个可能的扩展，该定理刻画了允许2-顶点连通方向的图。首先，我们证明了判定混合图是否具有2-顶点连通方向的问题是NP困难的。这回答了邦、黄、朱的一个问题。对于第二部分，我们称有向图D=（V，a）2T连通于某些T⊆V，如果D是2-arc连通的，并且D−V强连通于所有V∈T。我们从托马森定理中推导出了图的一个特征，它允许2T连通方向。

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

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.