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On the transversal Helly numbers of disjoint and overlapping disks |
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| Authors: | K. Bezdek T. Bisztriczky B. Csikós A. Heppes |
| Affiliation: | 1. Dept. of Math. and Stats, University of Calgary, 2500 University Drive N.W, Calgary, Ab T2N 1N4, Canada 2. Dept. of Geometry, E?tv?s University, Pázmány Péter sétány 1/c, H-1117, Budapest, Hungary 3. Vércse u. 24/A, H-1124, Budapest, Hungary |
| Abstract: | A family of disks is said to have the property T(k) if any k members of the family have a common line transversal. We call a family of unit diameter disks t-disjoint if the distances between the centers are greater than t. We consider for each natural number k≧ 3 the infimum tk of the distances t for which any finite family of t-disjoint unit diameter disks with the property T(k) has a line transversal. We determine exact values of t3 and t4, and give general lower and upper bounds on the sequence tk, showing that tk = O(1/k) as k → ∞. In honour of Helge Tverberg’s seventieth birthday Received: 9 June 2005 |
| Keywords: | 52A35 52A37 52A10 |
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