冗余全局刚性支撑三角剖分

IF 0.6 3区 数学 Q3 MATHEMATICS
Qi'an Chen, Siddhant Jajodia, T. Jordán, Kate Perkins
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引用次数: 0

摘要

通过将图G的顶点映射到r3中的点,将图G的边映射到相应的线段,我们得到了图G的三维实现。如果G的边长度唯一地决定了G的实现,那么G的实现就是全局刚性的,直到同余。如果图G的所有一般三维实现都是全局刚性的,则图G称为全局刚性。我们考虑支撑三角形的整体刚性特性,支撑三角形是通过添加额外的边(称为支撑边)从最大的平面图中得到的图。我们证明了对于每一个偶数n≥8,存在有3n−4条边的支撑三角形,如果从图中删除任意一条边,它仍然是全局刚性的。边界是最好的可能。这个结果对最近的一个猜想给出了肯定的答案。我们还讨论了我们的结果与S. Tanigawa和第三作者提出的一个相关的更一般的猜想之间的联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Redundantly globally rigid braced triangulations
By mapping the vertices of a graph G to points in R 3 , and its edges to the corresponding line segments, we obtain a three-dimensional realization of G . A realization of G is said to be globally rigid if its edge lengths uniquely determine the realization, up to congruence. The graph G is called globally rigid if every generic three-dimensional realization of G is globally rigid. We consider global rigidity properties of braced triangulations, which are graphs obtained from maximal planar graphs by adding extra edges, called bracing edges. We show that for every even integer n ≥ 8 there exist braced triangulations with 3 n − 4 edges which remain globally rigid if an arbitrary edge is deleted from the graph. The bound is best possible. This result gives an affirmative answer to a recent conjecture. We also discuss the connections between our results and a related more general conjecture, due to S. Tanigawa and the third author.
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来源期刊
Ars Mathematica Contemporanea
Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.70
自引率
0.00%
发文量
45
审稿时长
>12 weeks
期刊介绍: Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.
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