Trapezoids and Deltoids in Wide Planar Point Sets
We call a set of n points in the Euclidean plane “wide” if at most n of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is Ω ( n 3 log n ) and O ( n 3 log 2 n ) while for deltoids we have Ω ( n 5 / 2 ) and O ( n 8 / 3 log n ) .
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| Veröffentlicht in: | Graphs and combinatorics 2019-05, Vol.35 (3), p.569-578 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We call a set of
n
points in the Euclidean plane “wide” if at most
n
of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is
Ω
(
n
3
log
n
)
and
O
(
n
3
log
2
n
)
while for deltoids we have
Ω
(
n
5
/
2
)
and
O
(
n
8
/
3
log
n
)
. |
|---|---|
| ISSN: | 0911-0119 1435-5914 |
| DOI: | 10.1007/s00373-019-02009-2 |