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Long Alternating Paths Exist
[article]
2020
arXiv
pre-print
Let P be a set of 2n points in convex position, such that n points are colored red and n points are colored blue. A non-crossing alternating path on P of length ℓ is a sequence p_1, ..., p_ℓ of ℓ points from P so that (i) all points are pairwise distinct; (ii) any two consecutive points p_i, p_i+1 have different colors; and (iii) any two segments p_i p_i+1 and p_j p_j+1 have disjoint relative interiors, for i ≠ j. We show that there is an absolute constant ε > 0, independent of n and of the
arXiv:2003.13291v1
fatcat:7druoez6ifdvtmskmd3geyf6za