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Long Alternating Paths Exist
2020
International Symposium on Computational Geometry
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 p₁, ... , 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
doi:10.4230/lipics.socg.2020.57
dblp:conf/compgeom/MulzerV20
fatcat:5pdx7ifwmvchrczfcvsa6vk2pm