论平面图形的平面边长比

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2019-08-09 DOI:10.20382/jocg.v11i1a6

Manuel Borrazzo, Fabrizio Frati

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引用次数: 4

摘要

直线绘图的边长比是绘图中最长边和最短边的长度之比。平面图形的平面边长比是图形的任何平面直线绘制的最小边长比。本文研究了平面图的平面边长比。证明了存在$n$顶点的平面图，其平面边长比在$\ ω (n)$;这个界限很紧。我们还证明了几类平面图的边长比的上界，其中包括系列平行图和二部平面图。

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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On the planar edge-length ratio of planar graphs

The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight-line drawing of the graph. In this paper, we study the planar edge-length ratio of planar graphs. We prove that there exist $n$-vertex planar graphs whose planar edge-length ratio is in $\Omega(n)$; this bound is tight. We also prove upper bounds on the planar edge-length ratio of several families of planar graphs, including series-parallel graphs and bipartite planar graphs.

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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.