On the polygonal diameter (= link diameter) of the interior, resp. exterior, of a simple closed polygon in the plane

Micha A. Perles; Horst Martini; Yaakov S. Kupitz

doi:10.1016/j.dam.2013.01.018

On the polygonal diameter (= link diameter) of the interior, resp. exterior, of a simple closed polygon in the plane

Micha A. Perles
, Horst Martini^*
, Yaakov S. Kupitz

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a tight upper bound for the polygonal diameter (a.k.a. link diameter) of the interior, resp. exterior, of a simple n-gon, n≥3, in the plane as a function of n, and describe ann-gon (n≥3) for which both upper bounds (for the interior and for the exterior) are attained simultaneously.

Original language	English
Pages (from-to)	1576-1585
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	161
Issue number	10-11
DOIs	https://doi.org/10.1016/j.dam.2013.01.018
State	Published - Jul 2013

Keywords

Jordan exterior (interior)
Jordan's curve theorem
Jordan-Brouwer theorem
Polygonal diameter (= link diameter)
Raindrop proof
Simple closed polygon

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10.1016/j.dam.2013.01.018

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abstract = "We give a tight upper bound for the polygonal diameter (a.k.a. link diameter) of the interior, resp. exterior, of a simple n-gon, n≥3, in the plane as a function of n, and describe ann-gon (n≥3) for which both upper bounds (for the interior and for the exterior) are attained simultaneously.",

keywords = "Jordan exterior (interior), Jordan's curve theorem, Jordan-Brouwer theorem, Polygonal diameter (= link diameter), Raindrop proof, Simple closed polygon",

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AU - Perles, Micha A.

AU - Martini, Horst

AU - Kupitz, Yaakov S.

PY - 2013/7

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N2 - We give a tight upper bound for the polygonal diameter (a.k.a. link diameter) of the interior, resp. exterior, of a simple n-gon, n≥3, in the plane as a function of n, and describe ann-gon (n≥3) for which both upper bounds (for the interior and for the exterior) are attained simultaneously.

AB - We give a tight upper bound for the polygonal diameter (a.k.a. link diameter) of the interior, resp. exterior, of a simple n-gon, n≥3, in the plane as a function of n, and describe ann-gon (n≥3) for which both upper bounds (for the interior and for the exterior) are attained simultaneously.

KW - Jordan exterior (interior)

KW - Jordan's curve theorem

KW - Jordan-Brouwer theorem

KW - Polygonal diameter (= link diameter)

KW - Raindrop proof

KW - Simple closed polygon

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 10-11

ER -

On the polygonal diameter (= link diameter) of the interior, resp. exterior, of a simple closed polygon in the plane

Abstract

Keywords

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