Crossing-Free Perfect Matchings in Wheel Point Sets

International audience Given a set $P$ of $n$ points in the plane, where $n$ is even, we consider the following question: How many plane perfect matchings can be packed into $P$? For points in general position we prove the lower bound of ⌊log<sub>2</sub>$n$⌋$-1$. For some special configurations of point sets, we give the exact answer. We also consider some restricted variants of this problem.

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Point sets with many non-crossing perfect matchings

Computational Geometry ◽

10.1016/j.comgeo.2017.05.006 ◽

2018 ◽

Vol 68 ◽

pp. 7-33 ◽

Cited By ~ 2

Author(s):

Andrei Asinowski ◽

Günter Rote

Keyword(s):

Perfect Matchings ◽

Point Sets

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On the Intersection Number of Matchings and Minimum Weight Perfect Matchings of Multicolored Point Sets

Graphs and Combinatorics ◽

10.1007/s00373-004-0606-8 ◽

2005 ◽

Vol 21 (3) ◽

pp. 333-341 ◽

Cited By ~ 4

Author(s):

Criel Merino ◽

Gelasio Salazar ◽

Jorge Urrutia

Keyword(s):

Minimum Weight ◽

Intersection Number ◽

Perfect Matchings ◽

Point Sets

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Representation of certain self-similar quasiperiodic tilings with perfect matching rules by discrete point sets

Journal de Physique I ◽

10.1051/jp1:1994234 ◽

1994 ◽

Vol 4 (6) ◽

pp. 893-904 ◽

Cited By ~ 4

Author(s):

Richard Klitzing ◽

Michael Baake

Keyword(s):

Perfect Matching ◽

Discrete Point ◽

Point Sets ◽

Self Similar ◽

Matching Rules ◽

Quasiperiodic Tilings

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Almost empty polygons

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.40.2003.3.1 ◽

2003 ◽

Vol 40 (3) ◽

pp. 269-286 ◽

Cited By ~ 4

Author(s):

H. Nyklová

Keyword(s):

Exact Results ◽

Point Sets ◽

Planar Point ◽

Convex Position ◽

Vertex Set ◽

Point Set ◽

Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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