最大度比图的划分

IF 4.5 3区管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Annals of Operations Research Pub Date : 2025-05-07 DOI:10.1007/s10479-025-06615-7

Valentin Bouquet, François Delbot, Christophe Picouleau

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引用次数: 0

摘要

给定一个图G和它的顶点集的一个非平凡分割\((V_1,V_2)\)，顶点的满意度\(v\in V_i\)是它在\(V_i\)中的封闭邻域的大小与其在G中的封闭邻域的大小之比。所有顶点的最差比率定义了分割的质量。我们将一个图的度比q(G)定义为所有非平凡分区上最差比率的最大值。我们给出了一些图类的q(G)的界和精确值。我们还展示了相关优化或决策问题的一些复杂性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Partition of graphs with maximum degree ratio

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Partition of graphs with maximum degree ratio

Given a graph G and a non trivial partition \((V_1,V_2)\) of its vertex-set, the satisfaction of a vertex \(v\in V_i\) is the ratio between the size of it’s closed neighborhood in \(V_i\) and the size of its closed neighborhood in G. The worst ratio over all the vertices defines the quality of the partition. We define q(G) the degree ratio of a graph as the maximum of the worst ratio over all the non trivial partitions. We give bounds and exact values of q(G) for some classes of graphs. We also show some complexity results for the associated optimization or decision problems.

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来源期刊

Annals of Operations Research 管理科学-运筹学与管理科学

CiteScore

7.90

自引率

16.70%

发文量

596

审稿时长

8.4 months

期刊介绍： The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.