几何图形分解成星形森林

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-03-18 DOI:10.1016/j.comgeo.2025.102186

János Pach , Morteza Saghafian , Patrick Schnider

引用次数: 0

摘要

我们解决了dujmovovic和Wood（2007）的一个问题，证明了n个顶点上的完整凸几何图不能被分解成少于n−1个星林，每个星林由不相交的边组成。这个界限显然很紧。我们还讨论了抽象图的类似问题。

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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Decomposition of geometric graphs into star-forests

We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than

n - 1

star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.

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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.