Flips in odd matchings

IF 0.7 4区计算机科学 Q4 MATHEMATICS Computational Geometry-Theory and Applications Pub Date : 2025-12-01 Epub Date: 2025-03-13 DOI:10.1016/j.comgeo.2025.102184

Oswin Aichholzer , Anna Brötzner , Daniel Perz , Patrick Schnider

引用次数: 0

Abstract

Let

P

be a set of

n = 2 m + 1

points in the plane in general position. We define the graph

G M_{P}

whose vertex set is the set of all plane matchings on

P

with exactly m edges. Two vertices in

G M_{P}

are connected if the two corresponding matchings have

m - 1

edges in common. In this work we show that

G M_{P}

is connected and give an upper bound of

O (n^{2})

on its diameter. Moreover, we present a lower bound of

n - 2

and an upper bound of

2 n - 2

for the diameter of

G M_{P}

for

P

in convex position.

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在奇数配对中投掷

设P是平面上一般位置上n=2m+1个点的集合。定义图GMP，其顶点集是P上所有平面匹配的恰好m条边的集合。在GMP中，如果两个对应的匹配有m−1条共同的边，则两个顶点是连通的。在这项工作中，我们证明了GMP是连通的，并给出了其直径的上界O（n2）。此外，我们给出了P在凸位置的GMP直径的下界n−2和上界2n−2。

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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