Upper and Lower Bounds on Long Dual Paths in Line Arrangements
نویسندگان
چکیده
Given a line arrangement A with n lines, we show that there exists a path of length n/3−O(n) in the dual graph of A formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring such that it has an alternating path of length Ω(n/ logn). Our results also hold for pseudoline arrangements. ar X iv :1 50 6. 03 72 8v 1 [ m at h. C O ] 1 1 Ju n 20 15
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