Point sets with many non-crossing perfect matchings
نویسندگان
چکیده
منابع مشابه
Point sets with many non-crossing perfect matchings
The maximum number of non-crossing straight-line perfect matchings that a set of n points in the plane can have is known to be O(10.0438) and Ω∗(3n). The lower bound, due to Garćıa, Noy, and Tejel (2000), is attained by the double chain, which has Θ(3/n) such matchings. We reprove this bound in a simplified way that uses the novel notion of down-free matchings. We then apply this approach to se...
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Let Pn be a set of n m points that are the vertices of a convex polygon and let Mm be the graph having as vertices all the perfect matchings in the point set Pn whose edges are straight line segments and do not cross and edges joining two perfect matchings M and M if M M a b c d a d b c for some points a b c d of Pn We prove the following results about Mm its diameter is m it is bipartite for e...
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It is well-known that the number of non-crossing perfect matchings of 2k points in convex position in the plane is Ck, the kth Catalan number. Garćıa, Noy, and Tejel proved in 2000 that for any set of 2k points in general position, the number of such matchings is at least Ck. We show that the equality holds only for sets of points in convex position, and for one exceptional configuration of 6 p...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2018
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2017.05.006