Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 249257 (2009) 

On the Hadwiger numbers of centrally symmetric starlike disksZsolt LángiDepartment of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4, email: zlangi@ucalgary.caAbstract: The Hadwiger number $H(S)$ of a topological disk $S$ in ${\mathbb R}^2$ is the maximal number of pairwise nonoverlapping translates of $S$ that touch $S$. A conjecture of A. Bezdek., K. and W. Kuperberg [BKK] states that this number is at most eight for any starlike disk. A. Bezdek [B] 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. [BKK] Bezdek, A.; Kuperberg, K.; Kuperberg, W.: Mutually contiguous translates of a plane disk. Duke Math. J. {\bf 78} (1995), 1931. [B] Bezdek, A.: On the Hadwiger number of a starlike disk. In: Bárány, I. (ed.) et al., Intuitive Geometry Bolyai Soc. Math. Studies {\bf 6} (1997), 237245. Keywords: topological disk, starlike disk, touching, Hadwiger number Classification (MSC2000): 52A30, 52A10, 52C15 Full text of the article:
Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.
© 2008 Heldermann Verlag
