Problem

Source: BMO&IMO TST

Tags: geometry, combinatorics unsolved, combinatorics, Probabilistic Method



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