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On Inducing Polygons and Related Problems
"... Bose et al. [1] asked whether for every simple arrangement A of n lines in the plane there exists a simple ngon 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(n log n) time. In fact, we show that every finite family of cu ..."
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Bose et al. [1] asked whether for every simple arrangement A of n lines in the plane there exists a simple ngon 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(n log n) 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 Hamiltoniantype property: the union of the curves in C contains a simple cycle that visits every curve in C exactly once.
On Inducing ngons
 CCCG
, 2011
"... In this paper, we establish a lower bound on the number of inducing simple ngons in gridlike arrangements of lines. We also show that the complexity associated with counting the number of inducing ngons in an arrangement of collinear segments is #Pcomplete. ..."
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In this paper, we establish a lower bound on the number of inducing simple ngons in gridlike arrangements of lines. We also show that the complexity associated with counting the number of inducing ngons in an arrangement of collinear segments is #Pcomplete.