Abstract
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 \(\left\lfloor {\tfrac{{5n}} {{47}}} \right\rfloor \). This bound can be further improved to \(\tfrac{{3n - 1}} {{28}} \) for infinitely many n.
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Communicated by Imre Bárány
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Bhattacharya, B.B., Das, S. Disjoint empty convex pentagons in planar point sets. Period Math Hung 66, 73–86 (2013). https://doi.org/10.1007/s10998-013-9078-z
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DOI: https://doi.org/10.1007/s10998-013-9078-z