On some monotone path problems in line arrangements

Balogh, 2004, Long monotone paths in line arrangements, Discrete Comput. Geom., 32, 167, 10.1007/s00454-004-1119-1 Dey, 1998, Improved bounds for planar k-sets and related problems, Discrete Comput. Geom., 19, 373, 10.1007/PL00009354 A. Dumitrescu, Monotone paths in line arrangements with a small number of directions, Discrete Comput. Geom., submitted for publication Edelsbrunner, 1987 Edelsbrunner, 1989, Topologically sweeping an arrangement, J. Comput. System Sci., 38, 165, 10.1016/0022-0000(89)90038-X Erdős, 1935, A combinatorial problem in geometry, Compositio Math., 2, 463 Erdős, 1960, On some extremum problems in elementary geometry, Ann. Univ. Sci. Budapest, 3–4, 53 Matoušek, 1991, Lower bounds on the length of monotone paths in arrangements, Discrete Comput. Geom., 6, 129, 10.1007/BF02574679 Matoušek, 2002 Pach, 1995 Radoičić, 2003, Monotone paths in line arrangements, Computational Geometry, 24, 129, 10.1016/S0925-7721(02)00136-0 Tóth, 2001, Point sets with many k-sets, Discrete Comput. Geom., 26, 187, 10.1007/s004540010022 G. Tóth, P. Valtr, The Erdős–Szekeres theorem: upper bounds and related results, Manuscript, 2004 Welzl, 1986, More on k-sets of finite sets in the plane, Discrete Comput. Geom., 1, 95, 10.1007/BF02187686