Drawing outerplanar graphs using thirteen edge lengths

IF 0.4 4区计算机科学 Q4 MATHEMATICS Computational Geometry-Theory and Applications Pub Date : 2023-03-01 DOI:10.1016/j.comgeo.2022.101964

Ziv Bakhajian , Ohad Noy Feldheim

引用次数: 0

Abstract

We show that every outerplanar graph can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it.

This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmović, Morin and Wood.

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使用13个边长度绘制外平面图形

我们证明了每个外平面图都可以线性嵌入到平面中，使得相邻顶点对之间的不同距离的数量最多为13，并且顶点的图像和不包含它的边的图像之间没有交集。这扩展了Alon和第二作者的工作，在该工作中，只有顶点之间的重叠是不允许的，从而解决了Carmi、Dujmović、Morin和Wood提出的问题。

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

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.

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