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Edge-Removal and Non-Crossing Perfect Matchings
[article]
2011
arXiv
pre-print
We study the following problem - How many arbitrary edges can be removed from a complete geometric graph with 2n vertices such that the resulting graph always contains a perfect non-crossing matching? We first address the case where the boundary of the convex hull of the original graph contains at most n + 1 points. In this case we show that n edges can be removed, one more than the general case. In the second part we establish a lower bound for the case where the 2n points are randomly chosen.
arXiv:1107.2314v1
fatcat:tm2mfs6dizesvb2lpescx2vn4q