Bibliographic Details
| Title: |
Line Transversals in Large T (3)- and T (4)-Families of Congruent Discs. |
| Authors: |
Aladar Heppes1 |
| Source: |
Discrete & Computational Geometry. Sep2008, Vol. 40 Issue 2, p312-318. 7p. 7 Diagrams. |
| Subjects: |
Line geometry, Geometric congruences, Diameter, Distance geometry, Discrete geometry, Differential geometry |
| Abstract: |
Abstract A family of closed discs is said to have property T(k) if to every subset of at most k discs there belongs a common line transversal. A family of discs is said to be d-disjoint, d≥1, if the mutual distance between the centers of the discs is larger than d. It is known that a d-disjoint T(3)-family ℱ of unit diameter discs has a line transversal if . Similarly, a d-disjoint T(4)-family has a line transversal if . Both results are sharp in d, i.e., they do not hold for smaller values of d. The main result of this paper is that while the above lower bounds on d cannot be relaxed in general, some reduction of d can be compensated by imposing a proper d-dependent lower bound on the size of the family in both cases. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
