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

Authors:
Micha A. Perles;Horst Martini;Yaakov S. Kupitz
Affiliations:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel;Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany;Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
Venue:
Discrete Applied Mathematics
Year:
2013

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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.