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A combinatorial geometry problem

Source: BMO&IMO TST

December 31, 2011
geometrycombinatorics unsolvedcombinatoricsProbabilistic Method

Problem Statement

Given a set LL of lines in general position in the plane (no two lines in LL are parallel, and no three lines are concurrent) and another line ℓ\ell, show that the total number of edges of all faces in the corresponding arrangement, intersected by ℓ\ell, is at most 6∣L∣6|L|.
Chazelle et al., Edelsbrunner et al.
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