A Note on Toeplitz' Conjecture

被引：3
|
作者：
Pettersson, Ville H. [1 ]
Tverberg, Helge A. [2 ]
Ostergard, Patric R. J. [1 ]
机构：
[1] Aalto Univ, Dept Commun & Networking, Sch Elect Engn, Aalto 00076, Finland
[2] Univ Bergen, Dept Math, N-5008 Bergen, Norway
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2014年 / 51卷 / 03期
基金：
芬兰科学院;
关键词：
Chordless cycle; Depth-first search; Grid graph; Inscribed square; Jordan curve; Toeplitz' conjecture; CURVES;
D O I：
10.1007/s00454-014-9578-5
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In 1911, Toeplitz made a conjecture asserting that every Jordan curve in contains four points forming the corners of a square. Here Conjecture C is presented, which states that the side length of the largest square on a closed curve that consists of edges of an nxn grid is at least times the side length of the largest axis-aligned square contained inside the curve. Conjecture C implies Toeplitz' conjecture and is verified computationally for n <= 13.
引用
收藏
页码：722 / 728
页数：7
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