Abstract
Let P be a set of points in the plane and let T be a maximum-weight spanning tree of P. For an edge (p, q), let Dpq be the diametral disk induced by (p, q), i.e., the disk having the segment pq as its diameter. Let DT be the set of the diametral disks induced by the edges of T. In this paper, we show that one point is sufficient to pierce all the disks in DT. Actually, we show that the center of the smallest enclosing circle of P is contained in all the disks of DT, and thus the piercing point can be computed in linear time.
| Original language | American English |
|---|---|
| Pages (from-to) | 3-10 |
| Number of pages | 8 |
| Journal | Journal of Graph Algorithms and Applications |
| Volume | 28 |
| Issue number | 3 |
| DOIs | |
| State | Published - 10 Sep 2024 |
Keywords
- Fingerhut's Conjecture
- Helly’s Theorem
- Maximum spanning tree
- Piercing set
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- General Computer Science
- Computer Science Applications
- Geometry and Topology
- Computational Theory and Mathematics