Bose et al. (2003)  asked whether for every simple arrangement A of n lines in the plane there exists a simple n-gon P that induces A by extending every edge of P into a line. We prove that such a polygon always exists and can be found in O(nlogn) time. In fact, we show that every finite family of curves C such that every two curves intersect at least once and finitely many times and no three curves intersect at a single point possesses the following Hamiltonian-type property: the union of the curves in C contains a simple cycle that visits every curve in C exactly once.
Bibliographical noteFunding Information:
Research by Eyal Ackerman was supported by a fellowship from the Alexander von Humboldt Foundation . Research by Rom Pinchasi was supported by the Israeli Science Foundation (grant No. 938/06 ).
- Inducing polygons
- Line arrangement
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics