Bibliographic Details
| Title: |
Helly-Type Theorems for Line Transversals to Disjoint Unit Balls. |
| Authors: |
Otfried Cheong1, Xavier Goaoc2, Andreas Holmsen3, Sylvain Petitjean4 |
| Source: |
Discrete & Computational Geometry. Mar2008, Vol. 39 Issue 1-3, p194-212. 19p. 2 Diagrams. |
| Subjects: |
Integral theorems, Integrals, Integral calculus, Fractional integrals |
| Abstract: |
Abstract  We prove Helly-type theorems for line transversals to disjoint unit balls in â d . In particular, we show that a family of nâ¥2d disjoint unit balls in â d has a line transversal if, for some ordering ⺠of the balls, any subfamily of 2d balls admits a line transversal consistent with âº. We also prove that a family of nâ¥4dâ1 disjoint unit balls in â d admits a line transversal if any subfamily of size 4dâ1 admits a transversal. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
