On the tree-width of knot diagrams

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2018-09-06 DOI:10.20382/jocg.v10i1a6

S. Schleimer, A. D. Mesmay, J. Purcell, E. Sedgwick

引用次数: 11

Abstract

We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to give the first examples of knots where any diagram has high tree-width. This answers a question of Burton and of Makowsky and Mari\~no.

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在结图的树宽度上

我们证明了结图的小树分解可以导出相应结的小球分解。反过来，这意味着结承认一个小的基本平面子午面或一个小的桥球。我们用它来给出结点的第一个例子，其中任何图都有很高的树宽。这回答了伯顿、马可夫斯基和马里的一个问题。

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.