Disjoint Empty Convex Pentagons in Planar Point Sets

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Statistics Papers
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convex hull
discrete geometry
empty convex polygons
Erdős-Szekeres theorem
pentagons
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Mathematics
Statistics and Probability
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Bhattacharya, Bhaswar B
Das, Sandip
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In this paper we obtain the first non-trivial lower bound on the number of disjoint empty convex pentagons in planar points sets. We show that the number of disjoint empty convex pentagons in any set of n points in the plane, no three on a line, is at least āŒŠ5n/47āŒ‹. This bound can be further improved to (3nāˆ’1)/28 for infinitely many n.

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2016-03-01
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