On the Classification of Motions of Paradoxically Movable Graphs

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2020-03-25 DOI:10.20382/JOCG.V11I1A22

Georg Grasegger, Jan Legerský, J. Schicho

引用次数: 8

Abstract

Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown recently that a graph has flexible edge lengths if and only if the graph has a special type of edge coloring called NAC-coloring. We address the question how to determine all possible proper flexible edge lengths from the set of all NAC-colorings of a graph. We do so using restrictions to 4-cycle subgraphs.

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论悖论可动图的运动分类

如果平面上存在无限多个满足这些边长度的图的非全等实现，则图的边长度称为挠性。最近已经证明，当且仅当图具有一种称为nac -着色的特殊类型的边着色时，图具有柔性边长度。我们讨论了如何从一个图的所有nac着色的集合中确定所有可能的适当的柔性边长度的问题。我们使用对4循环子图的限制来做到这一点。

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

International Journal of Computational Geometry & Applications 数学-计算机：理论方法

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms. Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.