Bounds on the edge-length ratio of 2-outerplanar graphs

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-03-27 DOI:10.1016/j.comgeo.2025.102192

Emilio Di Giacomo , Walter Didimo , Giuseppe Liotta , Henk Meijer , Fabrizio Montecchiani , Stephen Wismath

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引用次数: 0

Abstract

The edge-length ratio of a planar straight-line drawing Γ of a graph G is the largest ratio between the lengths of every pair of edges of Γ. If the ratio is measured by considering only pairs of edges that are incident to a common vertex, we talk about local edge-length ratio. The (local) edge-length ratio of a planar graph is the infimum over all (local) edge-length ratios of its planar straight-line drawings. It is known that the edge-length ratio of outerplanar graphs is upper bounded by a constant, while there exist graph families with non-constant outerplanarity that have non-constant lower bounds on their edge-length ratios. In this paper we prove an

Ω (\sqrt{n})

lower bound on the local edge-length ratio (and hence on the edge-length ratio) of the n-vertex 2-outerplanar graphs. We also prove a constant upper bound on the edge-length ratio of Halin graphs, pseudo-Halin graphs, and their generalizations.

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2-外平面图边长比的界

图形G的平面直线图Γ的边长比是Γ的每对边的长度之比的最大值。如果这个比率是通过只考虑与一个公共顶点相关的边对来测量的，我们就讨论局部边长比。平面图的（局部）边长比是其平面直线图的所有（局部）边长比的最小值。已知外平面图的边长比上界有一个常数，而存在外平面度为非常数的图族，其边长比下界为非常数。本文证明了n顶点2-外平面图的局部边长比的Ω(n)下界，从而证明了n顶点2-外平面图的边长比。我们还证明了Halin图、伪Halin图及其推广的边长比的一个常数上界。

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.