On the Hadwiger Numbers of Centrally Symmetric Starlike Disks

نویسنده

  • ZSOLT LÁNGI
چکیده

The Hadwiger number H(S) of a topological disk S in R 2 is the maximal number of pairwise nonoverlapping translates of S that touch S. A conjecture of A. Bezdek., K. and W. Kuperberg [2] states that this number is at most eight for any starlike disk. A. Bezdek [1] proved that the Hadwiger number of a starlike disk is at most seventy five. In this note, we prove that the Hadwiger number of any centrally symmetric starlike disk is at most twelve. MSC 2000: 52A30, 52A10, 52C15

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تاریخ انتشار 2008