周期框架的可实现维度

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-04-29 DOI:10.1016/j.comgeo.2025.102200

Ryoshun Oba, Shin-ichi Tanigawa

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引用次数: 0

摘要

Belk和Connelly引入了有限图G的可实现维数rd(G)，它是最小非负整数d，使得任意维上的每一个框架（G,p）在rd中都有一个具有相同边长的框架。他们用禁忌次元描述了可实现维数最多为1、2或3的有限图。本文考虑周期框架，并将其推广到z对称图。我们给出了可实现维数最多为1或2的z对称图的一个禁忌小特征，并证明了当图被给定为商z标记图时，该特征可以在线性时间内得到检验。

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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Realizable dimension of periodic frameworks

Belk and Connelly introduced the realizable dimension

rd (G)

of a finite graph G, which is the minimum nonnegative integer d such that every framework

(G, p)

in any dimension admits a framework in

R^{d}

with the same edge lengths. They characterized finite graphs with realizable dimension at most 1, 2, or 3 in terms of forbidden minors. In this paper, we consider periodic frameworks and extend the notion to

Z

-symmetric graphs. We give a forbidden minor characterization of

Z

-symmetric graphs with realizable dimension at most 1 or 2, and show that the characterization can be checked in linear time when a graph is given as a quotient

Z

-labeled graph.

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.